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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 44, page id 797435492:0076
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618. 61.
L F C T. V.
simplicibus triplicatas substiendo rationes, est. y O. OBC YP
PB. _ his aequà les rationes adjungendo est ()N. v.  + r(. OBC
PA. Y P i YP. PB; hoc est GN. OBL PN. P. B. compo-
nendoque BN. OBE BN. PB. ergo OH - D PB. unde rursIIS
liguet rectam X O iplis AB; Z P interjacere: L, F. D.
ZVII. Consimili prorsus argumentatione constabit obliguio-
rum incidencium retractos ultra punctum Z iplam R. N interse-
CaTC.
ZV ITI. Ouinimo rursus exertiis apparet nonnili binos refractos
in eodem puncto convenire.
ZIX. Addo cum ipsO RN concurrentes retractos circa punctum
L conglomerari, praeserrim illos, qui ad partes F (obdiquius) inci-
dentes perrinene.
Nam accipiantur, exempli causa, sibi pares NS, ST; _ SIE BP
quarta proportionalis in ratione ZB ad BN; SB  quarta provorrionalis
in ratione YB ad BS; _ BR itidem quarta talis in ratione Y B ad
BT; _ a punctis P, O R crecta perpendiculares ipsam H R. L
secent in Z, Z, CV. patet (emox octensis) omnium spario VIS
incidentium retractos cum N R concurrere intra L Z; nec non omnes
ipsi S T incidentium refractos intra XV cum eodem conrenire, POr-
ro rectae BP, Ba, BR se habent invicem ut Cubi rectarum BH.
BS, BT, (vel sunt in ipsarum BHI, BS, B T ratione triplicata: nam
BF. TB:: BN cab. BY cab. e TB. BG:: Y Bcub. BScub.
adeoque exx quo B P. B :: B N cub. BS cub. d consimili ratione
BF. BR:: B AICuB. B Pcub.) unde faciie monstrabitur esse PO
multo minorem quam OR; XelZ X quam X V (verbis parco multis
in re Paris manitesta). Quare dicti retracti circa punetum Z. spissius
ipsum NR decustabunt.
32. X. Ex his demim conficitur: omnibus bene LHIIIaus, Cus
(0) centrum habenti in refracto NK uspiam constituro, puncti A
imaginem ad ipsum conditione predicum toties incinuata punctum L
contistere. Sit enim C D puxillx (in plano AB C jacens) Diameter.
axi Opcico RN perpendicularis; ec per ejus extrema C, D transeane
retracti IM LK ipli R N occurrentes punctis X, V. ex octensIS, patet
omnium inera spatium M _ incidentium radiorum re ractos intrater-
inos Z. X principulem retractum incersecare; neque non omnes ad
spatium