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# Title: [Physica, Id Est, Scientia Rerum Corporearum, In Decem Tractatus Distributa] Physica, Id Est, Scientia Rervm Corporearvm, In Decem Tractatvs Distribvta (shelfmarks Leibn. Marg. 7:1-2; ZEN Leibn. Marg. 7:1-2)
# Folio 228, page id 779785487:0286
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=779785487&page=286
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 90 lines, status machine
# Lines: 90 recognised, mean confidence 0.90
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

P ET ZSICAE T R ACF. FIE.
conus BOD, qui est ad AFF, in Ia ABL, qam TaNGAE AHI, CUIUS
ErixIiCaCa BD, AE; hoc ClE NE CD-
bus BD, ad cubum AF; ve enim SIE
requalis verimque rensio, debec (u-
pertcies conica BOD, hoc est pla-
RU BLD, TenTu in BGD, else ad
Tuperticiem conicam AFF, hOc CA
ad planum AE, cenTUM IN APF, VE
iplum est planum BD, ad planum
AE; ve iam de chordis dictum est.
si enim planum, BD; non cenlum,
est Tubquadruplum AE, non ren(I;
Cerre BOD rentum, Cs Tubguadeu
plum AFE rensI; rE patet; pari
modo diameter AF, renta In AFF,
est dupla diameeri BD, cenla in
BOD; igirur BC Cubdupla AF;
icemque C; dupla BC; ergoCC
Tubdupla, CF; igieur criangula
AFF, BOD une proporrionalia;
isitur e coni proporrionales; led
coni proportionales lunt re cylin-
dri proporrionales; hi VeFO, VE
cubi diamerrorum basis, vel alti-
rudinum, ve constat ex Ccome-
eria; igitur spacia decurla à planis
circularibus aeque rensIS, TunE in
triplicata dinmerrorum; igieur de
cuElum a BD, est ad decurlum ab.
AE, VE conUS BGD, ad COnU AFF,
Id Cst, vE 1. 2d 5.
Oninto, hinc racio Fonorum de-
terminari porest, secundum acu-
tum de graie; cum enim Coni se-
cundum actum de grane; COrpO-
rum aque renlorum; SinE in ea-
eione subduplicata spatiorum, Peu
vibrationum, id est, ve temporas
quibus hune vibrariones, Ccilicee
permutando s. Line praedicta plana
circularia, maius scilicet quadeu-
pluno minoris; lcque Epatium ina-.
ioris octuplum. Spacii minoris; hOc.
818. 58. polico. CE quadracum A M; cuius.
axis HIEBL, Cubdupla BM, Cicque
ABL, spacium minus, seu ribra
rio minor, cuius cempus (C AB,
Hat Cemiparabola ADF octupla Ce-
miparabola ABL, Cub eadem can-
GenTC AFT; haud dubic ADF, re-
Praelencabit spacium maius, id cAt,
Octuplum, cuius renipus erie AV,
igicur Fonus plani minoris, est ad
Ponum plani maioris quadrupli, ve
AD, ad AB; ve aurem habeatur
AD, CIE MI NI aequalis AM, duCaEUE
AN, EM MK; aqualis AN, acti.
MaEUE AD, aequalis AR, dico quod
Lemiparabola ADF, cM octupla al.
cerius ABC; Cunc enim Cemipara-
bola proporcionales, re quadrata
axium, vel applicatarum; isieur
Lemiparabola ABL; cAt ad ADP,
re quadeatum AB, ad quadrarum
AD. Sed quadraci Tub AB, duplum
est quadeatum (ub AM; huius re
i0, duplum guadearum Cub A N
vel NK; huius demum duplum,
quadracum sub AR 3 vel aequali
AD; igicur quadracum lub AD est
octuplum quadrari lub AB; isitur
Cemiparabola ADF est octupla le
nipacabola AB L; eodem modo
Procedacur in quanis alia plano.
rum aguerentorum rarione; iIXFa:
hanc regulam; ducatur planu
quodlibet in Tuam diameerum, pro-
ducta lune spacia; Cunc aurem. (0-
ni, re radices quadr. producto-
rum perimurando; v. 9. sic planum
A, 4. B, 1. diameter A, Clt 2. B, ve-
ror. ducatur quodliber planum in
Tuam diametrum, Ccilicet 4. In 2. 8
1. In P. ratio productorum est =..
IGIEUE CONIS A, eC ad COnCIM B vEF2-
dix quadrara 1. ad tadicem quadca-
tam 8. pari modo sc planum A 9.
dias omalis sIF AM, Ct Semixarabo diaetet 3,. B verO. 4.. diaMeTCF 2..
duCan