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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis (shelfmarks Leibn. Marg. 100:1/2, Stück 2; Leibn. Marg. 100:1/2)
# Folio 865, page id 851708439:0889
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TRTGONOMETELA PBANA.
Ergo postquam supputaci tuerinc Sinus omnes usque ad 60, dabuneur reliqui uf.
que 2d 90 per Lolam additionem. C. 3. 5570 53 ==563.
Racius cll. = chorda 60. ergo :I = 530, et (per 2) dancur Sinus semiltium
250. 77 30. 3345. 2752730 56,25. 28, 7,30 24, 3745
17 X9521
30. 3, 30750925. 2, 457 28 77 30. 52744333 45. Adeo UE
duodecima diritione perreniamus ad Sinus qui eandem habene rarionem ac areUS.
Sinus enim penulcimus elt ultimi duplus senlibilicer; nempe poluo Radio parcium
2.00000,00000, ne una iplarum detieie Sinus penustimus a duplo ulcimi. Sed
280OX L= 30 = 2048+52,44337 45. Ergo 1800. 2048:: arc 527443
8 45. arc L:: 552744, 3345
ST.
Invento Sinu unIuS minuti, quaeraTuT (per 3) SinuS 2 minutorum; cum (ver 4)
Sinus irium; Scc. ulque ad 30. Gradus; cum (Per 5) usque ad 60. Tum (per 6) usque
2d90.
Piera ee Cellibrandus quaerunt Sinus per Sectionum angularium AnalyFin: cu-
jus loco Pitiscus e Alii quibus Agebra nOn erat aque expedica, actribent Re-
culam P’alsi.
Daris Sinibus, inveniuntur Fangentes de Secantes sic. FF. PB:: F. A. BM. ee
FF. F B:: F A. P M. _BM. BH:: F G. GI. 1. C. Z. R:: S. P, _Z. R:: R. s. _ T.
R: : R. 7. vel permutando FF.. P A:: FB. BM:: FCE. BM:: GI. VB:: VI. PM.
2. c. 2. S:: R. F:: T. R::0. s.
T. F. M M A. T.
ZVR = S9Z ArO = 3S, ArCX IZ ArC.
2. EB. BN:: AB. FB:: (= AB) BN. SFB. 1. C. Y. 52 ArC:: 53 Ac. L R. Er5O
EVR = 59: Arc.
20. Z A L. BN:: AF. AB:: BN. BA. CrBO E A ExBa =BN 9, 1. C. 3S ArC Y Y
2 AC = 592 AC.
L F. M M A TI.
=RV = 2.93  = 2S SICXT: ArC. Nam Z F D. F N:: F D. AD:: FN. FB.
ErGOZEDKEB = F NG. 2. F6. GZ:: AE. E.D. ErBOZ AFKGZ =3F. D
XF CF = F Vg.
L. F M M A IIT.
Fangentes 2 Arcuum A, B, sun suis Co. tangencibus reciproe provorrionales.
Nam L, A. R:: R. 7, A. _ T, B. R:: R. 5B. ErBOT, AXT, A = RXR = F, Bx
7, B. F18OF, A. Y, B:: 7, B. T, A.
L F. M M A IV.
Co. linus 2 Arcuum A, B sunc Secantibus reciproce proporrionales. NIam L. A. R::
R. s, A. _ Z, B. R:: R. SB. Rr8O Z A. Zy B:: s, B. Sy A.
Provorciones Prixonometrix cum Plana cum Splixriex resolvi Colent in quatuor
Axiomata seu Theoremata primaria.
avioma Primum.
In Friangulo Rectanoulo, E crus unum anguli Recti Fiat Radiue Circuli, Fs.
potenula exu Secansansuli adjacentis, ec crus alterum Pangens. Sin Fypocenula
tiat Radius, crura erunt Sinus ansulorum oppolitorum. V. 8. E AB sC Ractius,
AF. est Sccans angiili A, e B P. Fansens. Sin A F. Sic Racius, BF est Sinus anguli A,
e AB Sinus anguli F.
Deinde suppono duas quasris lineas in parribus Canonis numeratas, este sibi
proporcionales in alia quaris mensura aestimaris. C. 8. uc A. B Radius Parcium
700000, ad B P. Fansencem Anguli A (seu 30) partium 57735:: sic pedtum in A B
nuMCrS 273, 2d 523 Dedes in B L. FerC.
Ovecationum per Secantes mentionem rix feci, quia in cabulis Logaricmicis
PaTO OCCUTruNE: quas tamen E admililsem, proportiones Prisonometrix Planx e
Sphaerica magno numero possene rariari, quod praeltirie Clarius. Sed mihi sut,
ficie proportiones singulis calibus pociltimas extribuilse, quales luns quae Radium
habene in loco primo: e in hunc tinems secances semet alque verum induxi.
R PXFPF
In