Synopsis of Universal Geometry

F

Figure, defined 1 & 67
Rectilinear figure 12
First figure, rational and isoperimetric Isoperimetric figures are shapes that have the same perimeter but different areas. 67
Figure explaining refractions 539
Figure explaining the system of Aristarchus Aristarchus of Samos was an ancient Greek astronomer who proposed a sun centered model of the universe. 157
Laws of figures 67
Figured parallelepiped 87
Similar figures 18, and reciprocal figures
Inscribed solid figures 43
Reciprocal figures 67
The height of a figure 67
Properties of a figure 67 and following
Similar figures 67 & 68
Figures that fill a space 68
Figures inscribed in a sphere 99
Figures circumscribed around a sphere 100
Solid figures under conical surfaces 102
Solid figures within a portion of a sphere 102
Figures drawn around spirals 139
Figures of hyperbolas and ellipses 335
Figures that fill a space 368
The limit of contingency original: "Finis contingentiæ". This refers to the point of contact between a curve and a tangent line. 505
The circumference of the firmament 158
The firmament as a mirror 509
Various rivers mentioned 272
Focal points of mirrors projecting cylindrical light 508
Powers and proportions of focal points 509
The force of shears containing helices 470
Center of a frustum of a parabolic and hyperbolic conoid A frustum is the portion of a solid, such as a cone or pyramid, that remains after its upper part has been cut off by a plane parallel to its base. 421
Measures of a frustum of a pyramid 423
A frustum of a cone and its measure 424
Centers of the frustums of a pyramid and a cone 416
A solid frustum according to Archimedes 93
A frustum of a cylinder and a cone compared to a cylinder and a cone 121
A frustum of a pyramid, a cone, and a conoid 400
Double support of a balance scale 452
Foundation of Trigonometry 183
Hyperbolic spindles compared with other bodies A spindle is a solid generated by revolving a curve around a chord. 173

G

King Gelon 154, 164, & 165
The trigonometry of Gellibrand Henry Gellibrand was an English mathematician known for his work on trigonometry and navigation. 255
Geodesy of straight lines Geodesy is the science of measuring and monitoring the Earth's size and shape. 71 & 72
Geometry, defined 65
Geometric mean 366
How many German miles are in the circumference of the earth 260
The work of Ghetaldi Marino Ghetaldi was a Ragusan mathematician who applied algebraic methods to geometric problems. 388
The gibbus A term referring to a rounded or convex swelling. 83
The gnomon The part of a sundial that casts a shadow. 73
Laws of weights on oblique planes 445 and following.
From where the greater weight of bodies arises 399
Weights of bodies compared together 438 and following.
Description of gravity 398
Properties of gravity 398
Diameter of gravity 442
Centers of gravity 143

H

The dwellings of the earth according to Theodosius Theodosius of Bithynia was an ancient Greek astronomer who wrote on the geometry of the sphere. 246
Harmonic mean 306. And the opposite of the harmonic mean.
Faces of a pyramid 85. Of a prism 86.
The helices of a screw 470
The first and second revolution of a helix 132
The helix 66
Comparison of a hemisphere with a cone and a cylinder 414
Centers of gravity of hemispheroids 429 and following
Measures of hemispheroids 424 and following
Hercules the Geometer 131
Hermodorus, son of Pappus 392
Hexahedral prism 86
Hexagonal honeycombs 368
How much faster a man's head moves than his feet This likely refers to the difference in rotational velocity due to the distance from the center of rotation. 398
How a man is able to stand 435