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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 72, page id 797435492:0296
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L RCF. YZ.
icerlecans, uc expressum vides; eAtque jam PR. PL:: (a) M. V
 (b) GF. GF(O)E PE. PFC PR. PF; quare P L = I P F
ItuE Flyperbola L BL curram EB F cansit. Prorracta jam TB
CHITI ZZ Conveniat in R; CAEgLE TUM RZ. ZB:: BS. SP. unde
RL X ST = = BSX D.B= B5x SX. atqui PrOPteF DS. SX:: (d)
B5. ST, eAtDSxSY = BS XSZ. erGO RI XST =DSxSY
=DSx CX. vel RZ. CX:: DS. SI; ComposILEque RL. RZ
.CZ:: DS. DT:: (d) N. M:: CZ. CZ -t C X. ItaqVC
divisim estRZ. CZ:: C Z. CX. adeoque RZ =C Z. unde R B
hyporbolam L. BLransit; haec igitur (R BT) curram FBB, ipsI
L. B Lcontisuam, quoque tanget. quod erat ProPOTTum.
VII. Hinc (i persistentibus reliquis, recta tantiim D P jum intex
DO, D F perpetuo Geomerrice media Ctaruatur (eodem qui prius tuit
ordinc) eadem BT curram F B F quoque conting et.
Frenim ex mediis ejuldem ordinis drithmetice Geometricéque pio-
portionalibus efformaex linex se mutuo continsumt, adcoque commu-
ni rectaransente saudent.
VIII. Porro (stantibus reliquis ut in postrema) quodris in curra
FB F designetur punctum F, qux curram ad hoc tanset recta simili
Pacto deterinatur.
Connectatur urique recta D F curram P. B P. secans ad F; irem du-
catur D O ad DC. perpendicularis ipsam P O intersecans ad X; Hat
CrIaM D Z. DY:: N. M; e connectatur E Y; ipsi demim F P Pa-
rallela ducatur PZ; haec curram F B F continget.
Nam centro D per P ducatur circulus C F I; concipiaturque linca
E FHcalis, ut a D educta quacunque recta DI (qux circulum C F.
seceF In. I, CUrVa HI EHI in H, _x iptam FB P in L) SE pepertuo
DE eodem inter DI, D L ordine proporrionalis, quo D P inter D C,
DE; palam est tunc (e praecedence) quod recta F P curram HFH
tanget; verum ip(I HI E H (a) analosa est curra FB F; (b) quare
recta F Z curram P. B F quoque tansct.
Fxhinc nedum innumerarum spiralium; ac aliarum diversi generis
infinicies plurium cansentes quam prompre determinantur.
1Z. Hinc clarum est, (i dux linex F P F, F F F SiC ad se reteran-
cur, ut a puncto quodam. D uccunque projectis rectis D P F; habe-
ant le restx DB, uc quadrata ex ipsis D F, _ ad harum cerminos
cansanE curraS rect ES, F F; cum perpendicularibus ad ipas
DE.
oners. 40
Eect. VI.
b TI. Lect. VII.
cr. Lect. VII
aConstr.
E18. 98
9. Tect. VII.
b3. Lec. VIII.
218. 99.
et