# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851708439:0576
# Permalink to this reading: https://leibnizlegible.com/page/851708439:0576?run=74
# 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 552, page id 851708439:0576
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851708439&page=576
# Source image: https://digitale-sammlungen.gwlb.de/content/851708439/jpgs/default/00000576.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 55 lines, status machine
# Lines: 55 recognised, mean confidence 0.91
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

DE DECTIONIBUS
Cap. TII.
drantibus minoris, ductam in quadratum sui demptis duobus quadraris radii: sie
est subtensa differentiae a semicircumferentia (sive in excectu tire in detectu;) ad
subcensam arcus duadrupli.
75. Vel Cc: R.  = 2P:: F. D. Vel R. dC = 25:: A. D. HOC et,
76. Bt Radius; ad Cubum subtensae areus majoris quadrante sed minoris cri-
bus quadrantibus, divisum per quadratum radii, dempto auplo subtensa: sic est
subtensa Differentiae a semicircumferentia; ad subtensam arcus duadrupli.
SC
C = 2P = C = P: EL (Si arCUS S EE major trIenL)
Rg 25 =C + S. ErSO, R. P + C:: F. D. (A R. 5 f c:: A. D. Hoc est,
78. e+ Radius; ad Recreeatum subtensarum areus tripti e simpli (majoris
triente, e minoris duobus trientibus;) si est subtensa Differentiae hujus areus a
semicircumferentia ad subtensam arcus Duadruph.
79. Sin arcus S, ucut major quactranre, sic minor crience; auc major duobus
eriencibus, sce nribus quacrancibus minor: Tum est p= = 25 =5 c. Adeo.
que R. S = C:: A. D. HIOC CA,
80. Ot Radius; ad subtensam arcus majoris quadrante, sed minoris triente,
(vel duobus trientibus majoris, sed minoris tribus, quadrantibus, dempta sub-
tensa tripli arcus: sic est subtensa Differentia hujus arcus a semicircumferentia
ad subtensam arcus duadrupl.
8I. Duae omnia sunc ab ipso Schemate manifesta. Obi chorda D, Subtendit
quadeupto arcuum A, E, P, S: et B subtendit duplo areuum E, P; et b dupto
areuum A, 5.
BE. Et in Ouadrilatero cujus latera B, D, sunc opposica et paralleta: _t C, C,
Oppolica; et P, P, rectae diagonales; Pq= Cg =BD; e Pg C4 = D. E
Timiliter, in Ouacrilatero ubi latera B D Func oppotica ee parallela; e CC latera
opposica; ee 55 diaeonales: 59 - c9 = bD, et 39 = C9 - D
83. Fr in eadem figura F9, ubi non tantum P, Sed _ arcuS S, Supponitur major
criente; duxe chordae S, S, (pariter ac P, P,) secane chorcam D.
84. Sed in altera tigura 20; ubi arcus S supponi.
tur major quacirante led minor triente; catus est
aliquanco diversus. Nam hic, areu b (Tubrenta
dupli arcus S) jacente ex altero latere ipsius D
(Tubrenlae quadrupli,) chorda D a chordis S non
LCCatuI.
85. Sed res eodem recidit: Nlam dua chordae
S S (live secem tive non secent chordam D)
cum non ingrediantur inseriptum quadrilaterum
(sed Tolummodo ostendunt b subrentam esse dupli
aECUS) CxIL utCUnque S9 - C9 = bD.
86. Eadem quae prius, postine alices demon-
Itrari (_ quidem commodius) hoc modo: Ni
mirum, (I, pro quadrilatero cujus quatuor latera
e dux diagonales TunE A, A, C, C, B, D; su
anEUIE A, A, B, B, C, D: (TumpciS TubtensIS Tim-
pli de dupli arcus bis; de cripli quadruplique se
mel:) cum eadem fere rarietate qua prius. Nam
R7. Si subrensa sumpli arcus A (vel F.) Sic mi-
nOx quadrante: cum A, B, _ A, D, crunt latera
oppolica; e B, C, diagonales. Adeoque CB = AB
= AD. EL Con sequienet 2 A -
=C- A
in