functionem solius
eam, in quam transit
per substitutiones
etc., patet determinantem functionis
fieri
![{\displaystyle =p^{m-2}y^{(m-1)(m-2)}r}](https://wikimedia.org/api/rest_v1/media/math/render/svg/abe112aceae60f68507258858fd5d9f06f3d2a30)
determinantem functionis
![{\displaystyle Z}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd)
autem
![{\displaystyle =P^{m-2}Y^{(m-1)(m-2)}R}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2b96eb3f70a5dcd45264fb982ba70b6afbf94b0c)
Quare quum per hypothesin
![{\displaystyle P}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a)
non sit
![{\displaystyle =0,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1fc73f4650c89ab3162da3193b1a57e041977b23)
res iam in eo vertitur, ut demonstremus,
![{\displaystyle R}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33)
certo identice evanescere non posse.
15.
Ad hunc finem adhuc aliam indeterminatam
introducemus, atque productum ex omnibus
![{\displaystyle (a+b-c-d)w+(a-c)(a-d)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/44a4c2fa4d6d5564e0a21b61d88e65bdba5872bd)
exclusis repetitionibus considerabimus, quod quum ipsas
![{\displaystyle c}](https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455)
etc. symmetrice
involvat, tamquam functio integra indeterminatarum
![{\displaystyle \lambda '''}](https://wikimedia.org/api/rest_v1/media/math/render/svg/26f8d1335f745d126a6eb922cc4675429c8541a4)
etc. exhiberi poterit. Denotabimus hanc functionem per
![{\displaystyle f(w,\lambda ',\lambda '',\lambda '''{\text{ etc.}}).}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0c664751fdd4056ec13374636ec2f6d8e2ee3a44)
Multitudo illorum factorum
![{\displaystyle (a+b-c-d)w-(a-c)(a-d)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91001dc8bb29db33eb463b42d6157b3afcb9cf30)
erit
![{\displaystyle {\tfrac {1}{2}}m(m-1)(m-2)(m-3)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b2dd3d1762908a764a301e09c67b8afe6cb5459d)
unde facile colligimus, fieri
![{\displaystyle f(0,\lambda ',\lambda '',\lambda '''{\text{ etc.}})=\pi ^{(m-2)(m-3)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bde09912cea02ba282a3265aff000430a97fa6bc)
et proin etiam
![{\displaystyle f(0,l',l'',l'''etc.)=p^{(m-2)(m-3)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e82518c7da7dde112bee16df7eec0818e1080313)
nec non
![{\displaystyle f(0,L',L'',L'''etc.)=P^{(m-2)(m-3)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e5de860924df1d8c515c3c55501c46fc6830b78a)
Functio
![{\displaystyle f(w,L',L'',L'''{\text{ etc.}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5d952a931daf5eed135b7a1bbf0a869b0a54bd7f)
generaliter quidem loquendo ad ordinem
![{\displaystyle {\tfrac {1}{2}}m(m-1)(m-2)(m-3)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b2dd3d1762908a764a301e09c67b8afe6cb5459d)
referenda erit: at in casibus specialibus utique ad ordinem inferiorem pertinere potest, si forte contingat, ut quidam coëfficientes inde ab altissima potestate ipsius
![{\displaystyle w}](https://wikimedia.org/api/rest_v1/media/math/render/svg/88b1e0c8e1be5ebe69d18a8010676fa42d7961e6)
evanescant: impossibile autem est, ut illa functio tota sit identice
![{\displaystyle =0,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1fc73f4650c89ab3162da3193b1a57e041977b23)
quum