indefinita incrementa
capere assumis quam ob causam etiam non dubito quin tua analysis, si penitius excolatur, ad multo profundiora mox sit perductura. Cujusquidem præstantiae jam eximia exempta a te feliciter confecta circa lineas citissimi appulsus ad datam lineam, quin etiam de methodo maximorum ad superficies applicata commemoras, quæ omnia ut accuratius persequaris, etiam atque etiam te rogo. Mea quidem methodo usus plures hujusmodi quæstiones circa superficies pertractavi in Scientia navali, quæ duobus voluminibus in-4o, Petropoli pluribus abhinc annis prodiit[1]. Quod autem ad tuam methodum, qua singulis applicatis
incrementa
tribuis, attinet, antequam hoc ipsum quod non aperte indicas, animadverti, de consensu tuarum formularum cum meis dubitaveram. Ut enim
fiat maximum, existente
![{\displaystyle d\mathrm {Z} =\mathrm {N} dy+\mathrm {P} d^{2}y+\mathrm {Q} d^{3}y+\ldots }](https://wikimedia.org/api/rest_v1/media/math/render/svg/bae0382000f8dcab4bca2e474ece646bc417b54f)
(ubi quidem pro
unitatem ponis, non pro
uti forte lapsu calami notas), necesse est id tuo signandi more sit
seu
At vero invenio ponendo tecum
pro ![{\displaystyle dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/845c817e348381a13f3fad5184169ce0e021c685)
![{\displaystyle {\begin{aligned}\delta \int \mathrm {Z} =&\int \left(\mathrm {N} -d\mathrm {P} +d^{2}\mathrm {Q} -d^{3}\mathrm {R} +\ldots \right)\delta y\\&+\left(\mathrm {P} -d\mathrm {Q} +d^{2}\mathrm {R} +\ldots \right)\delta y+\left(\mathrm {Q} -d\mathrm {R} +\ldots \right)d\,\delta y+\ldots \end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f691589efa8f97c37b97b552a4c3e9c01aeb67a)
et unde concludis esse debere
![{\displaystyle \mathrm {N} -d\mathrm {P} +d^{2}\mathrm {Q} -d^{3}\mathrm {R} +\ldots =0,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ecf049398236c10c892682f5c99b5ff01be9cdce)
cum tamen natura maximorum tantum postulet ut sit
![{\displaystyle \int \left(\mathrm {N} -d\mathrm {P} +d^{2}\mathrm {Q} -d^{3}\mathrm {R} +\ldots \right)\delta y=0,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2ab8a4ed851a82eb0bcdec8bdf35cc9df1e68d41)
Verum perspecta amplitudine
Si unicæ applicatæ
increm
![{\displaystyle \int \left(\mathrm {N} -d\mathrm {P} +d^{2}\mathrm {Q} -\ldots \right)\delta y\qquad \qquad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/722b67674a0dd5c09ec3a19613d681485a8a0ef1)
(
il y a ici urte grande déchirure)
partes
![{\displaystyle \left(\mathrm {P} -d\mathrm {Q} +d^{2}\mathrm {R} -\ldots \right)\delta y+(\mathrm {Q} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/b1f78464ced9cccc575564057c8ec1049dcb2c14)
![{\displaystyle x=a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aaae23950e96a955ab5b07015a168fd931d4d82b)
referantur, evanescere
sensus deprehendatur.
- ↑ Scientia navalis, seu tractatus de construendis ac dirigendis navibus. Petropoli, 1749, 2 vol in-4o.