Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 31v
Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.81.
Original at the GWLB · Page image · Annotations (IIIF) · Download text
One image of two folio pages side by side, registered by the library under both labels (also fol. 32r); this page is its left half.
The machine reads it as
- HZ
- XY ejusque abscissas
- Curva variari Yy refertur per ordinatas ad AXem AX. ducatur
- alius AXis A per idem punctum originis A, et sint ordruatae
- abscissam
- novae YC. Ex agatur normalis in L in A AX,
- et normalis GM in ordinatam YX. sit AL: LG: AP =
- Y M: MG: Y8 = b: C: C et eeL bb + cc
- fiet suit AX, X et YX, y et A∞, 8 er YG, W
- fiet ob AX = AL + M fint X = bG (1) + CW C M)
- ob XZ = XM -9L fint y wo (seu Y) - E (sen PL)
- fiat jam AG, g. parallela ipsi Y8 et per G ducatur GH paralleta
- ipsi AG e occurrens ipsi Y (si opis productae) in Z et sit
- Z; et Y7 V erit P- 9 + Z et W AP = Gu +HZ seu G = h +Z
- similitens
- N
- + v
- N∞ = YZL AC, seu W
- FZ seu comperio K +E∞- EZ
- etae sunt omnes varietates quarum capes unt ordinatae, quamdiu maneat
- ch, :C
- f+ k ist
- normales: =h+ Z et Z. 8- h - et Ex 4 et 5 fil Z = (5) - 8 -h et
- V = (11) =_ W - 9 ex 2 et 3 investigemns et W, Nempe ex 2 fit
- ex = CW _,: B = 8 Et ex 3 fit bW = Cy3: C =9, quos duos
- ralores equando fit cex - ccW = bb W F bey jam bb + cC = ee, fiet
- CCX = eeW = bey seu Cx + by f: e= W, quem valorem ipsius W substi-
- pendo in priore valore ipsius 8, fiatus, ee CCx = bcy, ibe = seu bbx - bcy, : b =
- sen ha ebs cbetincs; eu denique e bx = cy,: e=g. Hos valores 8 et o substituendo in b et 7
- X - = y - h et vC5 Cx +by - g
- Sit jam aequatio ad Conicam maxime variata, nempe
- data
- aa l aal a
- amzu =-amh A ambx - amc y
- +
- (13)
- u es
- anv = -ang + ancx + anby l
- ad dyus =2dEx + d+ xx
- pZV = ph9 = Pb9X + P Ch y p bb XyG + pbeXX - p bc yy
- = pehX - p bu y q- p cC xy se
- rata
- rZZ = rhh -2rblx + Erchus- Erbexy + rbbxx +r ec yy
- 192
- cam une epehe
- SWV = rgg = 2SCgX - 15b9y + 28bC xy + s ec XX + 5 bb yu
- ee
- Tollantur + primum X et y ope q et h.
- et xy ope b: c
- reliqua invenientur ope f, E, et q identificabuntur
- sed calculus iste, etsi in potostate sit, non est hujus loci umenim honagitur decedeliore
- aquedim adjauicam potius ex data ad conicam generaliscunte. ) S 2tX + + XX ducenda composita
- Hinc
- composilae datae ad simalicem
- quautum fieci potest facendo assamendo valores ipsius ipsarum et es seu qualex
- inventi supra aequ. 6,7,8, c. Nempe X = ft BZ + C∞ et y = K + v- EZ
- 2F x = + 2tf + +Z + 2tcb
- qee
- iuin
- eer qee
- gy = - KK + 2KC. Z - 2Kb∞ + 2bC vZ - 6b qqe = bb. v0
- o
- ee
- identificanda seu per compendium
- al + nZ + nV +Y 07 + = ZZ +s v0 = 0
- ordinatas jam mutemus in obliquas, pro YZ _ et parallelis, su ad abscissas HZ seu Z
- : ZH
- YI-
- ale
- ad hibendo Y V et paralletas, _. ad abscissas H seu . ita ut sit YZ
- fiet v: co d: a et ZW siu V- Z: cd = d i: a
- d: i: a et dd +ii ac
- seu v d co et X ) - 1 co, et fiet beb7 fiat X = f + b. 1 - bi co+ cdc
- ea
- et Y = K + bd c0 = C + Ci cd, et fiet x = + cd -bico + B ∞ et y + bd +cico - c V
- quae aquationes servient sistatum velimus transfonuare datam aequationem ad curvam nempe 19hoc loco.
- posito btrcqie
- vi et - C9,: b = h
- bg -ek: c 2h
- ref - ccg = bbg - b et
- seu cet = eeg - bek
- seu 9 = cf + bk,:
- bR + )
- et B et Bek-
- et = cf +bH ek:C
- ien h= Cf- cbkrcet, 1B
- et s-eef-as-cbr. dosciel y 11)
- bbF - bCK,: bC
- ergo ld demum hi- bf-ck; e)
- 0-
- 64
- reducenda ad dyus Ltx
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 31v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0062?run=74