# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/85138403X:0081
# Permalink to this reading: https://leibnizlegible.com/page/85138403X:0081?run=74
# Title: [Johannis Wallisii SS. Th. D. Geometriae Professoris Saviliani Oxoniae, Tractatus Duo] Johannis Wallisii SS. Th. D. Geometriæ Professoris Saviliani Oxoniæ, Tractatus Duo (shelfmark Leibn. Marg. 103)
# Folio 73, page id 85138403X:0081
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=85138403X&page=81
# Source image: https://digitale-sammlungen.gwlb.de/content/85138403X/jpgs/default/00000081.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
# Lines: 44 recognised, mean confidence 0.87
# 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.

 CCCDF
les: aequalia sune ergo Trionguta ANNY, AuM; _ GuoniaM BF
Parallela est ipsI S N, _ n C ipsi uM, aequalia Cunc eriam Trian-
gula ABD, ACK: aequales TunCigITUE AN _ Au; AM _ BS; AD
et Ax; AC e AB: quare dempris conrinuo aequalibuS, aequales
CTUNE NM X AS; ND _ SK; DC _nB.
Problema.
Data media erium proportionalium, _ differentia extrema
rum, dare exEreMtaS.
Sic media daca A D, eique ad rectos angulos POnatuT DZ X-
qualis difterentiae extremarum, _ dividatur bifariam inS, cen-
Ero autem S _ incerrallo S D describaEUL CIrCUIUS D UK, e Per S
ducta Au SX; PONAEUE AM aequalIS A_, _E AC. aqualis AK. Ouo
nia A D tansic circulum, ergo quadracum A D aequale eAt rect-
angulOpAK; CrGO AM, AD, AC, TunC in ConiUa PEOPOTTIONC,
ex MC. (diHerentIA exTremarU) aequalis est ipA DI.
Lemma.
Si fuerine magnicudines in intinitum decrelcentes SumnA
Differenciarum aequatur maximo Termino.
Sint Moenicudines aZ, b, c, dec, in infinicum: dico omnes
carum aifferencias aequari ipsi a2. Si RegeCUTSiNE MaIOICS, e
SIanE aB, 27, ds, c. aequales iPFIS b, C, d, C; CrUNE ergO
L. B, B7, 3 8, 6, Partes ipliuS aZ; non unc ergomajores T0-
10. Sinc jam minores, quare xequales line ipE Z s, reliquo autem ast
aequalis ponatur d, ipla eriam d Ponaeur ae minor; ergo addica
elt alia difterentia s E, quare Z E elt aequalis summae omniu diste-
remiari, ergo Z. s aqualis est ip(i ZC, major minori, quod est absur.
di.sErBOZ a (cum lic neque major neque minor) aequalis est sum-
mae omnium in infinicum differenciarum.
Lemma.
Dinarum magnicudinum differencia, aequalis es differentix
incer Cummim ee duplum urriulvis. Paret addendo aerique
IABMIEUdIML MIMLMAM, Vel UEEIQVC MAIAM.
Desinitio.
Polroonum Serratum est fgura constans alcernatim ex laceri-
bus sibi inricem parallelis, _ loceribus obliquis. Sola autemm la-
ceranon porallela voceneur simpliciter Lacero.
Polygonum Serracum circulo Circundas dicitur, quando
unusquisque angulus internus cir culam arcingII. Aeque idem cir-
culo inseri dicicur, quando unusqui sque angulUS ExTerNUIS CIrCU-
lur
5.
F18. 19.
8. T7