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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 19, page id 797435492:0227
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 F C 1t L1C
sonum puncta lineam constitment, saltem ad lineam contistent, ipsi
BC similem. Ductisenim quorlibet lateribus V B, VD, VE, VC
_ dueto plano CKL II ad planum BD F.C Parallelo, sine com-
munes plani V BD cum planis BC, CHI sectiones rectae BD, G HI.
hx parallelae erunr. Item communes plani V D F. cum iildem planis
BC, CH Sectiones DE, K L. Parallele erunt. Ergo anguli BDF
GRL sunt aquales. Irem se haber recta BD ad GK, UE D F ad
RL, quia urraque haec proportio aequalis est illi, quam habet V D 10.  Cen
ad VR (Cimilia quixre sune triansuta VDB, VRC, _ triangula
VDE, VRL) permutandoque BD. D F:: GR. RL. ergo omnes
subtense in CHI proportionales sunt subtensis omnibus in BC, eas
nimirum in utraque linea ordinacim ex deinceps accipiendo; d qua
sibimet adjacent in una parirer inflectuntur cum iis, quae sibi adjacent
inaltera. Frgo secundum superius insinuata lineasBC, O II limiles
esse CONSEaL. ) Ilinc eriam paret lineas curvas similes BC. GEEI Can-
dem ad se proporrionem habere, quam Superticierum, in eadem
qualibet recta lita, latera VB, VC. Duum enim subrensarum
iidem angulis inclutarum (uE BD, GR, vel DF, RL) Cingulx
rationes aequales sine rationi laterum V B, VG; etiam omnes AnEC I2. V. Flom.
cedentes conjuneta (hoc est FOta B C) ad omnes consequentes Con-
junctas (hoc CsttOTaM C HI) se habebuntur V B ad V C. Finc etiam
calimotu productarum superficierum emersit hxec proprietas; quod
intercepex scilicer a Parallelis ad BC planis, a verrice desumpia,
quibuscunque laceribus iisdem inclulae partes iplarum sine inter le s-
miles; uE puta Superticies BVC, OVHI; _E PVD, OVR.
(Ouod ex generali limilicudinis doctrina posthac explicanda luculen-
tius apparere porerie; interim ex similicudine lincarum currarum, e
earum cum Superticiei lateribus analogia, penitulque consimili superti-
cierum generatione latis elucescir; Paltem ex crianoulorum V BD
VGK. _E VDE, VRL, C calium omnium limilicudine satis con-
Rac; liquidem ex calibus infinitis triangulis utraque Superticies com-
Polita censeatur.) Unde Cimilium Superticierum proprierates iis con-
venient. Verum quod interceptas artinet a diverlis lateribus Super-
ficies, cas inter se comparando, notandum est quod balibus luis, seu
directricis linex respectiris partibus non semper proportionales lunt;
at Taltem hoc tum evenie, cum omnia dictx Superticiei larera lune
aequalia inter se, adeoque cum linea direCtrix eA peripheria circuli;
quo casu produeta Suverticies exir conica Superficies Aricte dicta,
rectumque quidem ad conum pertinens. Ouod si direcdris BC Tup-
ponatur c. 8. Peripheria circularis, laceraque sibimer inxqualia, si
diridatur
Lb. XL. FLeM.