CONTENTS 
ix 
pages 298-854 
;oda esta, 
> (s-c)} 
are root 
8, 9,10 
;ylinder 
sphere 
pyram it 
298-306 
307- 808 
308- 310 
310-314 
314-316 
316-344 
316-320 
320-344 
320-331 
320- 321 
321- 323 
323-326 
326 
326-329 
329 
330- 331 
331 
331- 335 
J VLCTKOs) 
t thereof 
1 Method’ 
on-cub 
mce and 
332 
332-334 
334 
334-335 
335 
335 
336-343 
341-342 
344 
344 
345- 346 
346- 352 
347- 348 
348- 349 
349- 350 
350- 351 
351 
351- 352 
352 
352- 354 
353- 354 
. 355-439 
on 
356 
356-357 
The Synagoge or Collection .... pages 357-439 
(n) Character of the work ; wide range . . . 357-358 
(/3) List of authors mentioned 358-360 
(y) Translations and editions 360-361 
(6) Summary of contents 361-439 
Book III. Section (1). On the problem of the two 
mean proportionals 361-362 
Section (2). The theory of means . . . 363-365 
Section (3). The ‘ Paradoxes ’ of Erycinus . . 365-368 
Section (4). The inscribing of the five regular 
solids in a sphere 368-369 
Book IV. Section (1). Extension of theorem of 
Pythagoras ....... 369-371 
Section (2). On circles inscribed in the ap^rfkos 
(‘shoemaker’s knife’) 371-377 
Sections (3), (4). Methods of squaring the circle 
and trisecting any angle ..... 377-386 
(a) The Archimedean spiral .... 377-379 
(S) The conchoid of Nicomedes .... 379 
(y) The Quadratrix 379-382 
(d) Digression : a spiral on a sphere . . . 382-385 
Trisection (or division in any ratio) of any angle 385-386 
Section (5). Solution of the vevcns of Archimedes, 
On Spirals, Prop. 8, by means of conics . . 386-388 
Book V. Preface on the sagacity of Bees . . 389-390 
Section (1). Isoperimetry after Zenodorus . . 390-393 
Section (2). Comparison of volumes of solids having 
their surfaces equal. Case of sphere . . . 393-394 
Section (3). Digression on semi-regular solids of 
Archimedes 394 
Section (4). Propositions on the lines of Archimedes, 
On the Sphere and Cylinder 394-395 
Section (5). Of regular solids with surfaces equal, 
that is greater which has more faces . . . 395-396 
Book VI. 396-399 
Problem arising out of Euclid’s Optics . . . 397-399 
Book VII. On the ‘ Treasury of Analysis ’ . . 399-427 
Definition of Analysis and Synthesis . . . 400-401 
List of works in the‘Treasury of Analysis’ . . 401 
Description of the treatises 401-404 
Anticipation of Guldin’s Theorem . . . 403 
Lemmas to the different treatises .... 404-426 
(а) Lemmas to the Sectio rationis and Sectio 
spatii of Apollonius 404-405 
(ft) Lemmas to the Determinate Section of 
Apollonius 405-412 
(y) Lemmas on the Niwety of Apollonius . . 412-416 
(S) Lemmas on the On Contacts of Apollonius . 416-417 
(e) Lemmas to the Plane Loci of Apollonius . 417-419 
(f) Lemmas to the Porisms of Euclid . . . 419-424 
(r]) Lemmas to the Conics of Apollonius . . 424-425 
(б) Lemmas to the Surface Loci of Euclid . . 425-426 
(i) An unallocated lemma 426-427 
Book VIII. Historical preface ..... 427-429 
The object of the Book 429-430 
On the centre of gravity ..... 430-433