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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 22, page id 797435492:0230
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 E C
ponitur ipsum triangalum rectanenlum VKD; _ c circulis ad quas
ceu radios descripris ipse conus contlatur. Frgo, disputat, ex ho-
rum circulorum peripheriis Superficios conica Componetur; quod
camen veritari comperitur adverlari; methodusque proinde Fallax
est. Rerono, male calculum hoc pactoiniri; e in peripheriarum e
quibus superficies constant computatione diverlam insticuendam esse
rationem ab ca, qua computantur linex quibus plana superficies con-
Cane, aut plana, e quibus corpora formantur. Nempe peripheria-
rum Superticiem curram constimentium e rerolatione prognatam
linex VD censeri deber e multitudine punctorum, qua sunt in ipsa
linea genetrice VD; quippe cum per ea lingula puncta tales peri-
pherixtranscane, nec plures rransire queant; quicunque lit axis, seu
lonsius distans, seu propius adjacens; axis enim Colummodo, pro
lonsiore vel propiore distantis politionéque raria, dictarum periphe-
riarum magnitudinem determinae. Verum mulcitudo linearum ex
quibus planum DV K supponitur constare, planorumque quibus
Solidum DV Y constat, c numero caxanda est punctorum in azc
VR; nec enim plures intra terminos V R Parallelae, ip(IV R perpen
diculares, rectae, vel plura calia parallela plana duci postunt, quam
horum punctorum mulcicudini xquinumera. Ouod oblerrando discri-
men (ledulo perpendendum) ommnem deritabimus errorem, e cur-
varum hajusmodi rot. en cenitarum Superficierum facillimo, reor
omnium quos rei nacura subministrat modo perquiremus. IIlum cor-
monstrabo. Pro reperienda v. 8. dimenlione curve superficiei linex
V D CirEa axem V R revolurione, concipiatur ipla VD in directum
extendi, ita scilicer ut ei exxquetur recta VD; _ ad ejus omnia
puncta rectae concipiantur applicari ipsi V D perpendiculares, e pe-
ripheriis circularibus, c quibus superticies curra contlatur, ordine
pares; lingulae lingulis, puta AX ipsi AY, _ C Z ipHI CY, ac
ita continuo. Frit ex his parallelis rectis constitutum planum V D X
aequale dicta currae superficier; hujulque partes illius parribus re-
spectiris. Sin loco peripheriarum applicentur iplarum respectiri radii
AZ, BZ, CZ, d reliqui; spatium ex his rectis constiturum (quae
Pane proportionali cum alteris serie procedunt) se habebit ad curvam
Superficiem, ut circuli onjusois radius ad eins circumferentiam. Un-
de liqua ratione deprehendi possit Summa radiorum peromnia lincae
generricis puncta transcuntium (hoc est si spatii VD Q dimensionem
reperire contiserit) eo ctatim ininorescet curva superficiei dimensto
In exemplum, Facilitaris ergo, proponacurconica Superficies D V Y
CrOtatu Procreata rectae V D, circa axem V R. Ad rectam VD ap-
plicentur
F18. 10,. I 17
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