Early English Books Online
 All Digital Collections  spacer  Login  
 
Add to bookbag
Author: Digges, Leonard, d. 1571?
Title: A geometrical practise, named Pantometria diuided into three bookes, longimetra, planimetra, and stereometria, containing rules manifolde for mensuration of all lines, superficies and solides: with sundry straunge conclusions both by instrument and without, and also by perspectiue glasses, to set forth the true description or exact plat of an whole region: framed by Leonard Digges gentleman, lately finished by Thomas Digges his sonne. Who hathe also thereunto adioyned a mathematicall treatise of the fiue regulare Platonicall bodies, and their Metamorphosis or transformation into fiue other equilater vniforme solides Geometricall, of his owne inuention, hitherto not mentioned of by any geometricians.
Rights/Permissions: The University of Michigan Library provides access to these keyboarded and encoded editions of the works for educational and research purposes. These transcriptions are believed to be in the public domain in the United States; however, if you decide to use any of these transcriptions, you are responsible for making your own legal assessment and securing any necessary permission. If you have questions about the collection, please contact eebotcp-info@umich.edu. If you have concerns about the inclusion of an item in this collection, please contact LibraryIT-info@umich.edu. This statement does not extend to any page images or other supplementary files associated with this work, which may be protected by copyright or other license restrictions. Please go to http://www.textcreationpartnership.org/ for more information.
Print source: A geometrical practise, named Pantometria diuided into three bookes, longimetra, planimetra, and stereometria, containing rules manifolde for mensuration of all lines, superficies and solides: with sundry straunge conclusions both by instrument and without, and also by perspectiue glasses, to set forth the true description or exact plat of an whole region: framed by Leonard Digges gentleman, lately finished by Thomas Digges his sonne. Who hathe also thereunto adioyned a mathematicall treatise of the fiue regulare Platonicall bodies, and their Metamorphosis or transformation into fiue other equilater vniforme solides Geometricall, of his owne inuention, hitherto not mentioned of by any geometricians.
Digges, Leonard, d. 1571?, Digges, Thomas, d. 1595. aut
Imprinted at London: By Henrie Bynneman, Anno. 1571.
Alternate titles: Pantometria
Subject terms:
Mensuration -- Early works to 1800.
Geometry -- Early works to 1800.
Surveying -- Early works to 1800.
URL: https://name.umdl.umich.edu/A20458.0001.001
How to cite: For suggestions on citing this text, please see Citing the TCP on the Text Creation Partnership website.

Table of Contents
View entire text
title page
To the right honorable my singular good Lorde Sir Nicolas Bacon Knight, Lord keper of the great seale of England.
The Preface to the Reader.
Elementes of Geometrie, or Diffinitions.
The first Chapter. Hovve Perpendiculares vppon any straight line are ereared,
The second Chapter. Hovve perpendiculare or hanging lines are dravven from a point assigned to any right line lying in the same playne Superficies▪
The third Chapter. From any point assigned to extende a Parallele to any other right line lying in the same Superficies.
Example.
The 4. Chapter. To diuide any limited right line into as many equall partes as ye list.
Example.
The 5. Chapter Hovv equall angles are made.
Example.
The 6. Chapter. To make a triangle equall to any other right lined triangle assigned.
Example.
The first Theoreme.
The seconde Theoreme.
The thirde Theoreme.
The fourth Theoreme.
The fifth Theoreme.
The sixth Theoreme.
The seuenth Theoreme.
The eight Theoreme.
The ninth Theoreme.
The tenth Theoreme.
The .7. Chapter. The description of the Quadrant Geometricall.
Of the Scale.
The .8. Chapter. The vse of the Scale, shewing perpendiculare or directe heightes by their shadowes.
The .9. Chapter. Of Vigetius concerning heigthes.
The .10. Chapter. VVithout shadovve or any supputation by your quadrant geometricall to take heigthes approchable.
The .11. Chapter. VVith the ayde of tvvo places to search out improcheable heightes.
Howe lengthes in heigth are knowen.
The 12. Chapter. Hovv by your Quadrant vvith calculation speedely to knovv all heightes accessible.
Example.
The .13. Chapter. To get inaccessible heightes by supputation (vvith the helpe of tvvo places) supposing either side of the Scale diuided, 100 partes.
By any two things of one length ioyned thus in right Angle, Altitudes are found.
The 14. Chapter. Heightes are ingeniously searched out by a staffe.
The .15. Chapter. Ye may also heereby redely measure all lengthes standing in heigth as the altitude of any Tovver standing on a hill, or the length of a steeple aboue the battlements, or the distance be∣tvveene story and story in edefices, your selfe standing on the grounde.
Beholde the Figure on the other side.
The .16. Chapter. By a Glasse heighthes may be pleasantly practized and founde on this vvise.
The .17. Chapter. To measure the deepenesse of any vvell by the Quadrant Geometricall.
The .18. Chapter. To get the length or distance of any place or marke in sight, be it neuer so farre, and that vvithout instrument.
Example.
The 19. Chapter. VVith halbardes, pikes or staues hauing no other instrumentes, you may measure the distance betvvene any tvvo markes lying in a right line from you, not approching any of them.
Example.
The .20. Chapter. To measure the distance betvveene any tvvo markes hovvsoeuer they be situate, thoughe there be riuers or suche like impedimentes be∣tvveene you, as ye cannot approche nighe any of them, and that vvithout instrument also.
Example.
The .21. Chapter Hovv ye may most pleasantly and exactely vvith a playne glasse from an highe cliffe, measure the distance of any shippe or shippes on the sea as follovveth.
Example.
The .22. Chapter. The making of an Instrument named the Geometricall square.
The .23. Chapter. You may redely hereby vvithout Arithmetike mete the distance of any marke.
Example.
The .24. Chapter. Hovv vvith your square Geometricall to tell any length so farre as ye may see by supputation.
Example.
The .25. Chapter. Hovv to mete any line Hypothenusall as the distance from your eye standing in a valley to the top of an hill or highe turret. &c.
Example.
The .26. Chapter. To measure the distance betvveene any tvvo markes lying in one plaine leuell ground vvith your eie or station hovve so euer they be situate vvithout supputation.
Example.
The .27. Chapter. The composition of the instrument called Theodelitus.
The .28. Chapter. To searche the beste proportion or simetrie of many places vvith the true distance approchyng neere none of them by the instrument named Theodelitus.
Example.
The .29. Chapter The construction of an instrument Topographicall seruing most commodiously for all manner mensurations.
The .30. Chapter. By this instrument to knovve hovv many myles or pase any Shippe is distante from you, your selfe standing vpon an highe cliffe or plat forme by the sea coaste.
Example.
The 31. Chapter. To knovv hovv muche higher or lovver any marke is than the leuell from your eye, although there be suche impediments betvvene, that you can neither approche nigh vnto it, nor see the base.
The .32. Chapter. To fynde the difference betvvene the streyght and cir∣cular or true vvater leuell from a fountaine at any place appoynted.
Example.
The .33. Chapter. You may also by this instrument meete the distance betvveene shippes on the sea, or other markes on the lande, hovv so euer they be situate, vvith the aid of Arithmeticall supputation.
Example.
The .34. Chapter. To dravv a platte of any coast or countrey, containing the true pro∣portion and Symetrie thereof, in suche sort that you may readely tell hovve farre any place is distant from other, and that vvithout Arithmeticke.
Example.
The Table.
The .35. Chapter. Hovv to reduce many plattes into one, and to make a fayre carde or mappe of an vvhole prouince or region, and that in as large or small roome as you vvil assigne, vvithout any arithmeticall calculation.
Example.
A note for sea Cardes.
A note for Mines.
The second kynde of Geome∣trie called Planimetra.
The fyrst Chapter. Of Triangles.
The right angled Isoscheles is thus measured.
Example.
A right angled Scalenum you shall thus mete.
Example.
The second Chapter. Any tvvo sides of right angled triangles knovven by calcula∣tion to finde the thirde.
Example.
The .3. Chapter. Ambligonium Isoscheles is thus measured.
Example.
Ambligonium Scalenum, you shall thus measure.
Example.
The 4. Chapter. Of Acutiangle Triangles called Oxigonia, there are three kindes.
Of Triangles Equilater.
Example.
Of Isoschele Acutiangle Triangles.
Example.
Of Oxigonium Scalenum.
Example.
The .5. Chapter. A rule generall to measure all manner Triangles according to their plaine.
The .6. Chapter. Of Squares.
Example.
Of rectangles or right angled Paralelogrammes.
Example.
Of Rhombus and Rhomboides.
Example.
The .7. Chapter. For measuring of lines perpendicular.
The .8. Chapter. To measure Trapezia.
Example.
The .9. Chapter. Rules to measure all equiangle superficies hovve many sides soeuer they haue.
Example.
An other Example.
A note to finde the centres of those equiangle Figures.
The .10. Chapter. To measure the Superficiall content of any rightlined Figure of vvhat forme so euer it bee,
The .11. Chapter. A readie mean to find the content superficial of any great field, or cham∣pion playne, hovv irregular of forme or fashion soeuer it bee, vvithoute painfull trauayling about it, onely by measuring one side.
Example.
A note for Wooddes.
The .12. Chapter. Hovve you maye from an highe Hil, or Cliffe, measure hovv manye Acres, Roodes, or Perches, is contayned in any Fielde, Parke, VVood, or other playne Superficies, in the countrie rounde aboute you, not approching nighe them.
Example.
The 13. Chapter. A note hovv to suruey an vvhole Region or playne champion Coun∣trey by the ayde of a playne pullished glasse.
The .14. Chapter. Of Circles.
The fyrst Theoreme.
The seconde Theoreme.
The thirde Theoreme.
Hovv the Area of a circle is founde.
Example.
Of the halfe circle.
Example.
Of the fragments or partes of a circle.
The .15. Chapter. There is a trianguler field hauing on the one side a vvell or foun∣tayne, this fielde must be equally diuided betvvene tvvo partie, and that in such sort that either of them may haue cōmoditie of that fountayn, not cōming on the others lande. I demaunde hovv that partition shall be made.
The .16. Chapter. To cut off from any triangular fielde as many acres, rodde or other measures, as shall be required, and that by a lyne dravvne from any angle assigned.
Example.
The .17. Chapter. To cut off from any triangular piece of grounde vvhat quantitie of perches ye lyste vvith a lyne equidi∣stant to one of the sides.
Example.
The .18. Chapter. For partition of Paralelogrammes vvhat kinde so euer they be of, note these Rules ensuing.
Example.
The .19. Chapter. To cut of from any Trapezium or Quadrangular peece of ground, vvhat part therof ye list.
Example.
The .20. Chapter. To diuide the superficies of any irregular Pollygonium, vvith a straight line proceeding from any one of the Angles assigned in suche sorte, that the partes shal retaine any proportion appointed.
The 21 Chapter. To diuide any irregular Pollygonium into as many equall partes as ye vvill desire, vvith right lines dravven from any poynt vvithin the superficies therof assigned.
Example.
The .22. Chapter. To diuide any circle vvhose semidiameter is knovven, vvith an other circumference concentricall, in tvvo suche partes that the one por∣tion to the other shal retayne any proportion assigned.
Example.
The .23. Chapter. The three sydes of a triangle knovven, by supputation to get the greatest circles semidimetiente that may be described vvithin that circle.
Example.
The .24. Chapter. To finde the greatest squares side that may be described vithin any triangle vvhose sides are knovven.
Example.
The thirde kynde of Geome∣trie named Stereometria.
The fyrst Chapter. To measure the contentes Superficiall and solide of any Prisma.
Example.
Beholde the Figure.
The .2. Chapter. Hovv the contents Superficiall and Solide of a Pyramis may be measured vvhether it be direct or declining.
Example.
The .3. Chapter. Hovv Cylinders and Cones are measured.
Example.
A note to finde the altitude of a Solide Cone.
The .4. Chapter. Hovve excauate or holovve tymber. &c. is measured.
Example.
The .5. Chapter. Hovve the crassitude and Superficies of a sphere is te bee measured.
Example.
The .6. Chapter. Hovve fragmentes or partes of a Globe are measured.
section
The .7. Chapter. Any sphericall segment propouned to atteyne the spheres dia∣ meter vvherof it is the fragment.
Example.
The .8. Chapter. Hovve a Pyramis cutte off, maye bee measured.
Example.
A note how by supputation to get the perpendiculares or altitudes of those Pyramides.
Example.
The .9. Chapter. To cut off from any Cone or Pyramis vvhat parte or portion thereof ye vvill desire, vvith a playne equedistante to the base, and to finde on vvhat parte of the solides side the section shall fall.
Example.
Here follovveth other fashioned bodies somevvhat straunge in figure, but in effecte those that tofore are measured.
The .10. Chapter. Hovv vvyne vesselles or barrels are measured.
An other mensuration of vessels more common.
Example.
Another note of measuring.
The .11. Chapter. One rule general exactly to measure al kinde of vvine vessels.
Example.
The .12. Chapter. Hovv by this small prepared vessell to measure the quantitie of the greater.
Example.
The .13. Chapter. Hovve both the liquour and default or emptinesse in vvine ves∣sels partly filled is to be moten.
Example.
The .14. Chapter. To measure exactly the solide content of any small body, hovv disordred or irregular so euer it be, the forme or fashion not regarded.
Example.
The 15. Chapter. Hovve the vvaight of any part or portion of a Solide body may be knovvne vvithout seperation therof from the body, vvherby it mought be paised or vvaighed in Ballance.
Example.
The Preface.
Diffynitions.
The second dffiinition.
The thirde diffinition.
The fourth Diffinition
The fifth diffinition.
The sixth diffinition.
The seuenth diffinition.
The eyght diffinition.
The ninth diffinition.
The tenth diffinition.
The eleuenth diffinition.
The twelfth diffinition.
The .13. Diffinition.
The fourtenth Diffinition.
The fiftenth Diffinition.
The .16. Diffinition.
The .17. Diffinition.
The .18. Diffinition.
The .19. Diffinition.
The .20. Diffinition.
The 21 diffinition.
The 22 diffinition.
The 23 diffinition.
The 24 diffinition.
The 25 diffinition.
The fyrst Probleme. To diuide any line or number by extreame and meane Proportion.
Example.
The fyrst Theoreme.
The 2 Theoreme.
The 3 Theoreme
The 4 Theoreme.
The 5 theoreme.
The .2. Probleme. The dimetiente of any circle giuen to searche out the sides or Cordes Trigonal, Tetragonal, Pentagonal & Decagonal.
Example.
Example.
The .3. Probleme. The side of any equiangle Triangle geuen, to finde out the Semi∣diameters of his containing and contained circles, vvith the true quantitie of the Area.
Example.
The .4. Probleme. The side of any square knovvne by supputation to attaine the Semidiamiters of his exteriour and interiour Circles, vvith the content of his plaine or Area.
Example.
The .5. Probleme. The side of any equiangle Pentagonum geuen by Arithmeticke to learne his circumscribing and inscribed circles Se∣midimetients vvith the exact quantitie of his plaine Superficies.
Example.
Other rules to perfourme the same.
Theoremes
The first Theoreme.
The second Theoreme.
The third Theoreme.
The fourth Theoreme.
The fifth Theoreme.
The sixt Theoreme.
The seuenth Theoreme.
The eyght Theoreme.
The ninthe Theoreme.
The tenthe Theoreme.
The eleuenth Theoreme.
The tvvelfth Theoreme.
The thirtenth Theoreme.
The fourteenth Theoreme.
The fifteenth Theoreme.
The sixteenth Theoreme.
The seuententh Theoreme.
The eyghtenth Theoreme.
The nyntenth Theoreme.
The 20 Theoreme.
The 21 Theoreme.
The 22 Theoreme.
The 23 Theoreme.
The 24 Theoreme.
The 25 Theoreme.
The .6. Probleme. The side of any Tetraedron giuen, to searche out the Se∣midiameters of the circumscribyng and inscribed spheres.
Example.
Theoremes of Tetraedron 1
The 2 theoreme.
The 3 Theoreme.
The 4 Theoreme.
The 5 Theoreme.
The 6 Theoreme.
The 7 Theoreme.
The 8 Theoreme.
The 9 Theoreme.
The 10 Theoreme.
The 11 Theoreme.
The 12 Theoreme.
The 13 Theoreme.
The 14 Theoreme.
The 15 Theoreme.
The 7. Probleme. The side of any Hexaedron giuen, to finde the semidimetientes of the contayning and contayned Spheres.
Example.
Theoremes of Hexaedron. 1
The 2 Theoreme.
The 3 Theoreme.
The 4 Theoreme.
The 5 Theoreme.
The 6 Theoreme.
The 7 Theoreme.
The 8 Theoreme.
The 9 Theoreme.
The 10 Theoreme.
The 8. Probleme. The side of Octaedron giuen, to searche out Arithmetically the con∣tayning spheres Diameter and the Axis therof.
Example of the firste.
Example of the seconde rule.
Example of the thirde precepte.
Theoremes of Octaedron. 1.
The second Theoreme.
The thirde Theoreme.
The fourth Theoreme.
The fifth Theoreme.
The sixth Theoreme.
The seuenth Theoreme.
The eight theoreme.
The ninth theoreme.
The tenth theoreme.
The eleuenth theoreme.
The tvvelfth theoreme.
The thirteenth Theoreme.
The fourtenth Theoreme.
The fiftenth Theoreme.
The .9. Probleme. The side of an Icosaedron measured, by supputation to finde his axis and contayning spheres dimetiente.
Example.
Theoremes of Icosaedron and his partes. 1.
The second Theoreme.
The thirde Theoreme.
The fourth Theoreme.
The fifth Theoreme.
The sixth Theoreme.
The seuenth Theoreme.
The eight theoreme.
The nynth Theoreme.
The tenth Theoreme.
The eleuenth Theoreme.
The tvvelfth Theoreme.
The 13 Theoreme.
The 14 theoreme.
The 15 theoreme.
The 16 theoreme.
The 17 theoreme.
The 18 theoreme.
The 19 Theoreme.
The 20 Theoreme.
The .10. Probleme. The side of Dodecaedron giuen, by calculation to finde his axis and conteyning spheres diameter.
Example.
Theoremes of Dodecaedron.
The seconde theoreme.
The third Theoreme.
The fourth Theoreme.
The fifth theoreme.
The 6 theoreme.
The 7 theoreme.
The 8 theoreme.
The 9 theoreme.
The 10 Theoreme.
The .11. Probleme. The side of Tetraedron knovvne to finde his superfi∣ciall and solide content.
Examples of the Superficiall quantitie.
Examples of the Solide capacitie.
Theoremes of Tetraedrons super∣ficiall and Solide contentes.
The second theoreme.
The third theoreme.
The fourth theoreme.
The fifth theoreme.
The sixth theoreme.
The seuenth theoreme.
The eight theoreme.
The ninthe theoreme.
The tenth theoreme.
The .12. Probleme. The side of a Cube measured, to finde his Su∣perficiall and Solide quantitie.
Example.
Example of the Solide content.
Theoremes of Hexaedrons super∣ficies and Crassitude. Theoreme first.
The second theoreme.
The third theoreme.
The fourth theoreme.
The fifth theoreme.
The sixth theoreme.
The seuenth theoreme.
The eight theoreme.
The ninthe theoreme.
The tenth theoreme.
The .13. Probleme. Octaedrons side giuen to searche his superficiall and solide contente.
Example.
The example of the solide content.
Theoremes of Octaedrons contente superficiall and solide. 1.
The 2 theoreme.
The 3 theoreme.
The 4 theoreme.
The 5 theoreme.
The 6 theoreme.
The 7 theoreme.
The 8 theoreme.
The 9 Theoreme.
The 10 Theoreme.
The .14. Probleme. The side of Icosaedron knowen, by supputation to learne the con∣tentes superficiall and solide of that bodie.
Examples of the former rules.
Theoremes of Icosaedrons contents superficiall and solide. 1.
The second Theoreme.
The 3 Theoreme.
The 4 Theoreme.
The 5 Theoreme.
The .15. Probleme. The side of Dodecaedron giuen, to searche out by Arithmeticall calculation the superficiall and solide contente.
Example.
Theoremes of Dodecaedrons Su∣perficiall and Solide quantities. 1.
The 2 theoreme.
The 3 theoreme.
The 4 theoreme.
The 5 theoreme.
The .16. Probleme. The diameter of any sphere knovven, to searche out the sides, Axes and contayning or contayned circles semidiameters of all suche bodyes regulare as are therein to be described, both Arithmeti∣cally and Geometrically.
Example.
Theoremes of the Regular bodyes in one containing sphere described. Theoreme first.
The second theoreme.
The third theoreme.
The fourth theoreme.
The fifth theoreme.
The sixth theoreme.
The seuenth theoreme.
The eight theoreme.
The nynth Theoreme.
The tenth Theoreme.
The eleuenth Theoreme.
The tvvelfth theoreme.
The thirtenth theoreme.
The fourtenth theoreme.
The fiftenth theoreme.
The 16 theoreme.
The 17 theoreme.
The 18 Theoreme.
The 19 theoreme.
The 20 Theoreme.
The 21 Theoreme.
The 22 theoreme.
The 23 theoreme.
The 24 theoreme.
The 25 theoreme.
The .17. Probleme. Arithmetically and geometrically to search out all the sides, diameters, perpendiculars, and lines Diagonall, vvith the bases semidiame∣ters, of all suche regular bodies as shall circumscribe or cōprehend any sphere vvhose dimetient is knovvn.
Example.
Geometrically to perfourme the same.
Theoremes of the internall Spheres circumscribing Solides. 1
The 2 Theoreme.
The 3 Theoreme.
The 4 Theoreme.
The 5 Theoreme.
The 6 Theoreme.
The 7 Theoreme.
The 8 Theoreme.
The 9 Theoreme.
The 10 Theoreme.
The 11 theoreme.
The 12 theoreme.
The 13 Theoreme.
The 14 Theoreme.
The 15 Theoreme.
The .18. Probleme. The side of any Tetraedron giuen, to finde the sides, Diameters, and Axes, of all such regulare bodyes as maye therein bee described.
Example.
Or thus geometrically without respect of number.
Theoremes of Tetraedrons inscribed solides. 1.
The second Theoreme.
The thirde Theoreme.
The fourth Theoreme.
The fifth Theoreme.
The sixth Theoreme.
The seuenth Theoreme.
The eight theoreme.
The ninth theoreme.
The tenth theoreme.
The .19. Probleme. The side of a Cube giuen, to finde the sides, diameters and axes of all suche regulare bodies as may therin be described.
Example.
Theoremes of Hexaedrons inscir∣bed regulare Solides.
The 2 theoreme.
The 3 theoreme.
The 4 Theoreme.
The 5 Theoreme.
The 6 Theoreme.
The 7 Theoreme.
The 8 theoreme.
The 9 theoreme.
The 10 Theoreme.
The .20. Probleme. Octaedrons side giuen, to searche out all his conteyned bo∣dies, sides, diameters and axes.
For Tetraedron.
For Icosaedron.
Examples of Tetraedron.
Of the Cube.
Of Icosaedron.
Theoremes of Octaedrons inscribed regular bodyes. 1.
The seconde theoreme.
The third Theoreme.
The fourth Theoreme.
The fifth theoreme.
The sixte Theoreme.
The seuenth Theoreme.
The eight theoreme.
The ninth Theoreme.
The tenth theoreme.
The .21. Probleme. Icosaedrons side geuen, in line or number to set forth all the sides, Diameters and Axes of his contained regulare bodyes.
Of Tetraedron.
Of Octaedron.
Of Hexaedron.
Theoremes of Icosaedrons inscribed bodyes. Theoreme first.
The second theoreme.
The third theoreme.
The fourth theoreme.
The fifth theoreme.
The sixth theoreme.
The seuenth theoreme.
The eyght Theoreme.
The ninthe Theoreme.
The tenth Theoreme.
The .22. Probleme. The side of any Dodecaedron giuen, both Arithmeticallye and Geo∣metrically to serche out the sides diameters and axis of all the re∣gulare bodies therin described.
Of Tetraedron.
Of Hexaedron.
Of Octaedron.
Of Icosaedron.
An example of Icosaedron.
Theoremes of Dodecaedrons inscribed regulare Solides.
The 2 Theoreme.
The 3 Theoreme.
The 4 Theoreme.
The 5 theoreme.
The 6 theoreme.
The 7 theoreme.
The 8 theoreme.
The 9 theoreme.
The 10 theoreme.
The 11 theoreme.
The 12 theoreme.
The 13 theoreme.
The 14 theoreme.
The 15 theoreme.
The 16 theoreme.
The 17 theoreme.
The 18 theoreme.
The 19 theoreme.
The 20 theoreme.
The 21 Theoreme.
The 22 Theoreme.
The 23 Theoreme.
The 24 theoreme.
The 25 theoreme.
The .23. Probleme. The side, Diameter or Axis of any regulare bodye knovven, to searche out all those forenamed lines in any regulare bodye that shall include or circumscribe that proponed solide.
Example.
Theoremes of these bodies mutually circumscribed and confer∣red vvith their inscribed regular bodies. 1.
The 2 theoreme.
The 3 theoreme.
The 4 Theoreme.
The 5 theoreme.
The 6 Theoreme.
The 7 Theoreme.
The 8 theoreme.
The 9 theoreme.
The 10 Theoreme.
The 11 theoreme.
The 12 Theoreme.
The 13 Theoreme.
The 14 theoreme.
The 15 theoreme.
The 16 Theoreme.
The 17 theoreme.
The 18 theoreme.
The 19 theoreme.
The 20 theoreme.
The 21 theoreme.
The 22 theoreme.
The 23 theoreme.
The 24 theoreme.
The 25 theoreme.
The .24. Probleme. The side, diameter, Axis, or altitude, of any regular body, or any se∣midiameter, perpendicular or line diagonall of their base giuen, to search out the content Superficiall and solide, not on∣ly of that body, but also of any other regular so∣lide that shall inscribe or containe that body or any of his spheres.
Rules for the content Superficiall and Solide of the fiue Regular bodyes.
For Tetraedron.
For Octaedron.
For Hexaedron.
For Icosaedron.
For Dodecaedron.
The fyrst question. I haue a Dodecaedron, vvhose comprehending spheres diameter I knovv to be fiue, I demaund his ca∣pacitie superficial and solide.
The second question. A cube is proponed, vvhose Diameter is the Zenzike roote of 108▪ I vvoulde knovve the superficiall and solide con∣tentes of such a Tetraedron as this Cubes con∣tayned sphere should circumscribe.
The thirde question. I demaund the superficiall and Solide capacitie of a Dodecaedron, circumscribing such an Octaedrons containing sphere, as hath for his side this irrationall Maior √{powerof2} v. 20+√{powerof2}387 ⅕.
The fourth question. There is a Dodecaedron, vvhose side is this irrationall Apotome √{powerof2} v. 1120—√{powerof2}1152000, my desire is to knovve his inscri∣bed Icosaedrons superficies and crassitude.
The fyfth question. An Icosaedron is offered, vvhose basis contayning circles semidimetient is this surde Binomye √{powerof2} vni. 14 14/15 +√{powerof2}204 ⅘ the superficies and crassitude of his contayning Dodecaedron is required.
Of Tetraedron.
theorem 1
The 2 theoreme.
The 3 theoreme.
The 4 theoreme.
The 5 theoreme.
The 6 theoreme.
The 7 theoreme.
The 8 theoreme.
The 9 theoreme.
The 10 theoreme.
Of Hexaedron.
The 11 theoreme.
The 12 theoreme▪
The 13 theoreme.
The 14 theoreme.
The 15 theoreme.
The 16 theoreme.
The 17 theoreme.
The 18 theoreme.
The 19 theoreme.
The 20 theoreme.
Of Octaedron.
The 21 theoreme.
The 22 theoreme.
The 23 theoreme.
The 24 theoreme.
The 25 theoreme.
The 26 theoreme.
The 27 theoreme.
The 28 theoreme.
The 29 theoreme.
The 30 theoreme.
Of Icosaedron.
The 31 Theoreme.
The 32 Theoreme.
The .33. Theoreme.
The .34. Theoreme.
The .35. Theoreme.
The .36. Theoreme.
The 37 Theoreme.
The .38. Theoreme.
The 39 Theoreme.
The 40 Theoreme.
Of Dodecaedron.
The .41. Theoreme.
The .42. Theoreme.
The .43. Theoreme.
The .44. Theoreme.
The .45. Theoreme.
The 46 Theoreme.
The 47 Theoreme.
The 48 Theoreme.
The 49 Theoreme.
The 50 Theoreme.
The .25. Probleme. A Metamorphosis or transformation of the fiue regulare bodies.
Of Tetraedron transformed. The firste Diffinition.
The firste Theoreme.
The 2 theoreme.
The 3 theoreme.
The 4 theoreme.
The 5 theoreme.
The 6 theoreme.
The 7 theoreme.
The 8 theoreme.
The 9 thorme.
The 10 theoreme.
The 11 theoreme
The 12 theoreme.
The 13 theoreme.
The 14 theoreme.
The 15 theoreme.
The 16 theoreme.
The 17 theoreme.
The 18 theoreme.
The 19 Theoreme.
The 20 Theoreme.
Of the transfigured Cube. The seconde Diffinition.
The 21 Theoreme.
The 22 theoreme.
The 23 theoreme.
The 24 theoreme.
The 25 theoreme.
The 26 theoreme.
The 27 theorome.
The 28 theoreme.
The 29 theoreme.
The 30 theoreme.
The 31 theoreme.
The 32 theoreme.
The 33 theoreme.
The 34 theoreme.
The 35 theoreme.
The 36 theoreme.
The 37 theoreme.
The 38 theoreme.
The 39 theoreme.
The 40 theoreme.
Of Octaedron transformed. The 3 Diffinition.
The 41 theoreme.
The 42 theoreme.
The 43 theoreme.
The 44 theoreme.
The 45 Theoreme.
The 46 theoreme.
The 47 theoreme.
The 48 theoreme.
The 49 theoreme.
The 50 theoreme.
The 51 theoreme.
The 52 Theoreme.
The 53 Theoreme.
The 54 theoreme.
The 55 theoreme.
The 56 theoreme.
The 57 theoreme.
The 58 Theoreme.
The 59 Theoreme.
The 60 theoreme.
Of the transfigured Icosaedron. The fourth Diffinition.
The 61 theoreme.
The 62 theoreme.
The 63 theoreme.
The 64 theoreme.
The 65 Theoreme.
The 66 Theoreme.
The 67 theoreme.
The 68 theoreme.
The 69 theoreme.
The 70 theoreme.
The 71 Theoreme.
The 72 theoreme.
The 73 theoreme.
The 74 theoreme.
The 75 theoreme.
The 76 theoreme.
The 77 theoreme.
The 78 theoreme.
The 79 theoreme.
The 80 theoreme.
Of Dodecaedron transformed. The fifthe Diffinition.
The 81 Theoreme.
The 82 Theoreme.
The 83 theoreme.
The 84 theoreme.
The 85 theoreme.
The 86 theoreme.
The 87 theoreme.
The 88 theoreme.
The 89 theoreme.
The 90 theoreme.
The 91 theoreme.
The 92 theoreme.
The 93 theoreme.
The 94 theoreme.
The 95 theoreme.
The 96 theoreme.
The 97 theoreme.
The 98 theoreme.
The 99 theoreme.
The 100 Theoreme.
Theoremes of these transformed bodyes conserred both vvith their circumscribing regular bodyes, and also betvveene them selues.
The 1 theoreme.
The 2 theoreme.
The 3 Theoreme.
The 4 Theoreme.
The 5 Theoreme.
The 6 Theoreme.
The 7 Theoreme.
The 8 Theoreme.
The 9 Theoreme.
The 10 theoreme.
The 11 theoreme.
The 12 theoreme.
The 13 theoreme.
The 14 theoreme.
The 15 theoreme.
The 16 theoreme.
The 17 theoreme.
The 18 theoreme.
The 19 theoreme.
The 20 theoreme.
The 21 theoreme.
The 22 theoreme.
The 23 theoreme.
The 24 theoreme.
The 25 Theoreme.
illustration
colophon