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Author: Gibson, Thomas, 17th/18th cent.
Title: Syntaxis mathematica, or, A construction of the harder problemes of geometry with so much of the conicks as is therefore requisite and other more ordinary and usefull propositions inter-mixed, and tables to several purposes / by Tho. Gibson.
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Print source: Syntaxis mathematica, or, A construction of the harder problemes of geometry with so much of the conicks as is therefore requisite and other more ordinary and usefull propositions inter-mixed, and tables to several purposes / by Tho. Gibson.
Gibson, Thomas, 17th/18th cent.
London: Printed by R. & W. Leybourne for Andrew Crook, 1655.
Subject terms:
Geometry -- Early works to 1800.
URL: https://name.umdl.umich.edu/A42708.0001.001
How to cite: For suggestions on citing this text, please see Citing the TCP on the Text Creation Partnership website.

Table of Contents
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title page
CONTENTS.
TO THE READER
ERRATA.
Preface.
Common Sentences.
I. Greater.
II. Lesse.
III. Equall things.
IV. Agréeing things.
V, Vnequall things.
VI. Double.
VII. Halfe.
VIII. A thing is.
IX. Something.
X. Nothing.
XI. Lesse then nothing.
XII. Vnity.
Propositions of EUCLIDE, fit to be known to the ANALIST.
Definitions.
Definition I.
Definition II.
Definition III.
Definition IV.
The names of the Potestates or Powers.
Consectary I.
Consectary II.
The Middle Part
Example.
CHAP. I. An explanation of the Characters and Symbols used in this Work.
In ADDITION.
In SƲBTRACTION.
Example.
In MƲLTIPLICATION.
In DIVISION.
CHAP. II. Of Aequations.
REDƲCTION
CHAP. III. Of the resolution of Aequations, according to the generall Method composed by Mr. Tho. Harriot.
The Resolution.
Of Cubicall Aequations.
The Resolution.
Of the resolution of Mixed Cubiques.
The Resolution.
NOTE.
Example of Devolution.
Resolution.
Example of Anticipation.
The Resolution.
Extraction of the greater Root.
2. Eduction of the lesser Root by Devolution.
COMPENDIUM 1.
Example also in Numbers.
COMPENDIUM 2.
CHAP. IV.
Rule 1.
Rule 2.
Example.
NOTE.
Rule 3.
Example.
NOTE 1.
NOTE 2.
NOTE. 3
Rule 4.
COMPENDIUN
NOTE.
CHAP. V. Of Reduction of Solids.
Example in Numbers.
NOTE.
Example in Numbers.
NOTE
CHAP. VI. Of Surd Numbers
Rule 1
Rule 2.
NOTE.
Rule 3.
MULTIPLICATION.
CONSECTARY.
NOTE.
Rule. 4 For ADDITION.
CHAP. VII.
Prob. 1.
Prob. 2.
Prob. 3.
COROLLARY.
NOTE.
Probl. 4.
COMPENDIUM.
RESUMPT.
NOTE.
CHAP. VIII. Of Mixtion.
DEFINITION. 1.
DEFINITION 2.
DEFINITION 3.
NOTE.
Prop. 1.
Prop. 2
Prop. 3.
Example in Numbers.
Rule. 1.
Rule. 2.
Rule. 3.
NOTE.
Prop. 4
Example in Numbers.
Prop. 5.
Prop. 6
Prop. 7.
Example in Numbers.
CHAP. IX. Of Mensuration.
The solidity of these other is found thus.
A Fragment.
The solidity of a Fragment (lesse then half a Sphere) is found thus.
Example.
The like for Cones in this case.
Otherwise thus.
Example.
DEMONSTRATION.
CHAP. X.
NOTE. 1
NOTE. 2
NOTE. 3
NOTE 4.
Otherwise, and more for Mcchanick use.
CHAP. XI. Definition generall of a Cone.
Definition 1.
Definition 2.
Definition 3.
Definition 4.
Definition 5.
Definition 6.
Definition 7.
Definition 8.
Definition 9.
CHAP. XII. Of the description of the Sections.
1. To describe a Parabola about any Diameter given with one of the ordinate lines.
2. About any Diameter, and one Ordinate line, to describe an Hyperbola known in kinde, in a plain by points.
3. About a diameter given, and an Ordinate, to describe by points in a plain; an Ellipsis known in kinde.
COROLLARY.
RƲLES.
To finde the Axis of a Parabola.
CHAP. XIII. To draw a tangent to any point assigned in any Section, or from any point without the Section.
NOTE.
Any Section given, to find that diameter thereof, which shall make an angle with the Ordinate to it, equall to an angle given.
Any Hyperbola being given, to finde the Asymptoti.
More for the Parabola. Numerically.
For an Hyperbola, Numerically.
For an Ellipsis, Numerically.
CHAP. XIV.
Probl. 1. Betwixt any two right lines given, as r and s, to finde two mean proportionals.
Prob. 2 Now secondly let it be required, to divide any rectiline angle given into three equall parts, as the angle bag.
NOTE.
The Demonstration of this Problem is as fol∣loweth.
NOTE. 1.
NOTE. 2.
Prob. 3.
DEMONSTRATION.
CHAP. XV.
Probl. 1.
DEMONSTRATION.
ADVERTISEMENT.
Probl. 2. Ʋpon a line given as a Base to describe an Isos∣celes triangle, so that an inward parallel Base may cut off two segments of the sides betwixt the bases, so that either segment may be equal to the inwad base, the perpendicular from the vertex to the said inward Base being also by supposition given.
Note 1.
NOTE 2. Mechanically.
NOTE. 3
CHAP. XVI. Of Dialling.
Probl. 1. Ʋpon any declining Plane, to finde the height of the Stile, and place of the Substile, the Decli∣nation being first known.
Probl. 2. Of Declining Recliners.
DEMONSTRATION.
NOTE.
Example.
Prob. 3. To find the same in those called South Declining Inclining Planes.
DEMONSTRATION.
Probl. 4. To draw any Verticall Dial by help of an Ho∣zontal dial, without any Aequator.
CHAP. XVII. Of the Perpendicular Stile.
Of the Signes, or Parallels.
Example.
Example.
Of the Vertical Circles.
Note 1.
NOTE. 2.
Almicanters
Of the Jewish, Babylonish and Italian hours.
CHAP. XVIII.
Rule. 1.
Rule. 2.
Rule 3
Example.
tables
First for the Table A.
Secondly, for the Table B.
Thirdly, for the Table C.
For the Table A.
For the Table B.
For the Table C.
To find the Declination of a Place.
To find the right Ascension of a Place.
To find the Ascensional Difference.
To find the, Oblique Ascension.
Note 1.
NOTE. 2.
tables
The second Table for 100 li. year rent, or Annuity.
The use of these Tables is thus.
NOTE.
Note 2.
Example.
Here followeth the third Table.
The construction of these Tables, or any other the like is as followeth.
Example in Interest 7 per cent.
Ʋse of the Tables.
Example 1. Interest profitable.
The Rule.
NOTE.
Example 2. Interest damageable.
The Rule.
Probl. 1.
Probl. 2.
Prob. 3.
Probl. 4.
Prob. 5.
Prob. 6.
table
Postscript.
RƲLE 1.
RƲLE 2.
RƲLE 3.
NOTE
A Rule for squaring binomiall surds, which should have been in Chap. 6. pag. 76.
Example in Numbers.