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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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4
PHILOSOPHILE NATVRALIS
DEMOTD Res. 4. Duoniam densitas Medii prope verticem FIyperbola
on major est quam in loco A, ur habeatur densitas medioeris, debee
ratio minimxe cangentium GT ad tangentem AFI inveniri, de
densicas in L augeri in ratione paulo majore quam semisumme
harum cansentium ad minimam tansentium I.
Reg. 5. Si dantur longitudines AH, AC, et describenda sit Figu-
xa GK: Produc (I N ad X, ut sIc PI X aequalis Facto suB n F 1 ec
AI: centroque d AIymptotis MX, N X ver punctum A describa-
tur IIyperbolas ea lege, uE sIc AI ad quamris V C VE X V ad XI
Rec. 6. Duo major est numerus n, co magis accuratae sunE HX
yperbola in ascensu corporis ab , ec minus accuratxe in ejus de-
Ecensu ad K; ec contra. LIyperbola Conica medioerem rationem
cenet, eAtque caeteris simplicior. Igitur li Fyperbola sic hujus generis,
ex punctum KC, ubi corpus projectum incidet in rectam quamris A il
per punctum A transcuntem, quaeratur: occurrat producta AW
ASIMPEOTIS MX, WVX in M X N, _ Cumatur NVK ipsi A M aequalis.
Rec. 7. Fc hinc liquet methodus expedita decerminandi hanc
TIpperbolam ex Phaenomenis. Projiciantur corpora duo limilia ee
aequalia, eadem velocitare, in angulis diversis HAK, B A P inci-
dancque in planum FTorizontis in RL _ k; EE ROTCtur prOxOrtiO AR
2d IR. Sic ca d ad e. Tum crecto cujulvis longicudinis perpen-
diculo I, altume uccunque longitudinem H vel Ah, et inde
collige graphice longitudines ALL, Ak, per RCg. 6. Si ratio AR
ad Ak lic eadem cum ratione d ad e, longitudo A recto antump-
ta FuIE. Sin minus cape in recta infinita SM longitudinem SM
aequalem aNumPEa AFI, et erise perpendiculum M N aequale ta-
tionum dicterentix == -- ductae in rectam quamris datam. Si
mili methodo ex alsumpris pluribus longitudinibus AFI invenien-
dta sunt plura puncta I, et per omnia 2-
Senda Curra linea regularis NNXN, SC-
cans rectam SMMM in X. ANumaEus
demum 1CI xqualis abscistae SX ec inde
denuo inveniatur lonsitudo H; ec lon-
sicudines, quae sint ad apumpeam longieu-
dinem AT ex hanc ulcimam AFY uc lonsicudo AR per experi-
mentum cosnita 2d ultimo inventam lonsitudinem AI, erunt renx
illae lonsirudines AY et AF, Quas invenire oporcuir. Hilce rero
datis dabitur ec resistentia Medii in loco A, quippe quae sic ad rim
Graritatis ut ATI ad 2AI. Ausenda eAt aurem densitas Mectii pen
RC5. 4; ee relstentia modo inventa, si in cademratione augeatur, Hec
accuratiOr.
Lute.