Synopsis of Universal Geometry

The page contains ink bleed-through from the reverse side and some spots of foxing, though the text remains legible.

The angle of refraction of the entering ray is equal to the refraction of the exiting ray, 580.
Annular [ring-shaped] body, 171
Ring of a circular section, 172
A handle is a suspended diameter, 442 original: "Ansa"
A yardarm as the cause of a ship's motion, 451
The Antitycho of Scipio, 559 A reference to Scipione Chiaramonti's work Antitycho, which defended traditional astronomy against Tycho Brahe's findings.
Antichthones, or Antipodes, 270 term: Antichthones (Antichthones) refers to legendary people living in the opposite hemisphere or on a "counter-earth."
Antoeci, and their oppositions on the sphere, same page. term: Antoeci (Antoeci) are people living under the same meridian but at the same latitude in the opposite hemisphere.
Apollonius's books 5, 6, and 7, in Golius, 274 The mathematician Jacobus Golius discovered and translated these books of Apollonius from Arabic.
The French Apollonius, 383 Likely referring to the mathematician François Viète, who reconstructed lost works of Apollonius.
The Arabic Apollonius, 274, his propositions.
Six apotomes defined, 38, and their properties, 39 term: Apotome (Apotome) is a mathematical term for a specific type of irrational line.
Properties of apotomes, 37
Thirteen lines following the apotome, 40
The industry of bees, 368 Mersenne explores the geometric efficiency of honeycomb structures.
More water is contained in a vessel at the foot of a mountain than at its peak, 399
Aqueous humor and others, 487 The aqueous humor is the clear fluid inside the front of the eye.
The bold saying of Archimedes, 395 A reference to Archimedes's claim that he could move the Earth with a lever given a place to stand.
Military architecture, preface, point 11.
Arcs smaller than a semicircle, 215
Arcs sharing boundaries with the base, 217
Arcs of spherical circles compared, 206, and following.
Arcs of true and apparent motion, 531
The area of spherical triangles compared to the greatest circle of the sphere, preface, point 6.
The number of grains of sand if the whole world were turned to sand, 164 Mersenne refers here to Archimedes's famous work, The Sand Reckoner.
How large a grain of sand is, 159
Aries, the first sign, 263
Aristarchus of Samos, 154, his celestial system, 154 Aristarchus was an ancient Greek astronomer who proposed a sun-centered universe.
Arithmetic mean, 366
Sculptural arts as parts of architecture, 541
The art of machines, 392 term: Mangana (Mangana) is a Greek-derived word for lifting engines or war machines.
True and apparent right ascension, 531
Deceptions of sight, 495

Asymptotes, 290 and 341
Properties of asymptotes, 291, and following.
The little star of Pancratius, 471 This likely refers to a specific mechanical device or a geometric figure named for a contemporary researcher.
Stars which rise, and those which do not, 250, and following.
The astronomy of Boulliau, preface, point 11. Ismaël Boulliau was a French astronomer and a friend of Mersenne.
Astronomical position, 370
Astronomical day, 265. Horizon, same page.
Astronomical or true horizon, 265
Attalus, 274 and 305 Attalus of Rhodes was a Greek mathematician known for his commentary on Aratus.
The colors of the dawn, 529
Autolycus on the moving sphere, 243 and following. Autolycus of Pitane wrote one of the oldest surviving Greek mathematical works on the motion of the heavens.
Conjugate axes, 278
Optical axes, where they are, 491
Axioms, or common notions, 3
Four axioms of magnitudes, 31
Six axioms for the solution of rectilinear triangles, 186
Four axioms for the solution of spherical triangles, 186
Axis of the cone and cylinder, 42
Axis of a solid, 85
The ends of the axis, the poles, 189
Axis and base of a cylinder.
Axis of a conic section, 333. Vertex.
Axis of the prism, cylinder, and pyramid, 400
Laws of the wheel and axle, 468 term: Axis in peritrochio (Axis in peritrochio) is a simple machine using a wheel and a central axle to lift loads.
Immutable common axis, 492
The nature of the optical axis, 488

A staff supported by a finger, 455
Baldi's opinion on the yardarm, 411 Bernardino Baldi was an Italian mathematician and historian of mechanics.
The base of a triangle in power, 75 In geometry, "power" often refers to the square of a line's length.
Base, height, and vertex of sections, 129
Use of the balance, or scales, 127
A binomial, or two names, 34
The Garisenda tower of Bologna, 436 A famous leaning tower in Italy used as a case study in structural stability.
The bulging [belly] of barrels, 177

What it is to be heated, 567
The perpendicular [cathetus] of incidence and reflection, 501