64
LIVRE I, SECTION II.
et par suite
; soit enfin
De
là nous avons :
![{\displaystyle \log \operatorname {tang} u.........}](https://wikimedia.org/api/rest_v1/media/math/render/svg/29ee471eb51a0115f8e6812ea9e73c63842af0ec) |
9,4630573 |
|
![{\displaystyle \log \sin(\lambda -{\text{☊ }})...}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4e95adb93729e769bd4a112a71038a943fec9695) |
9,4348691
|
![{\displaystyle \log \cos i...........}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5e57313ff23c0611d5e2239e2d85f0e729fb3dbf) |
9,9885266 |
|
![{\displaystyle \log \operatorname {tang} i........}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9eaea95b28fb7fdd25ef9451d261511a132835eb) |
9,3672305
|
![{\displaystyle \log \operatorname {tang} (\lambda -{\text{☊ }})...}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8e85c74e69f9f4ad76c558368286696324cba343) |
9,4515839 |
|
![{\displaystyle \log \operatorname {tang} \beta ........}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c463b69946f2a0c94a2384ef1bd92270cb512727) |
8,8020996
|
195° 47′ 40,25″ |
|
3° 37′ 40,02″n
|
306° 55′ 28,98″ |
|
![{\displaystyle \log \cos \beta .........}](https://wikimedia.org/api/rest_v1/media/math/render/svg/20149ebf313e7895953367b55b57c3a4b2ea2974) |
9,9991289
|
![{\displaystyle \log r..............}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ef3b95d6cfd88b7781ca81018674c0d797e8d2e8) |
0,3259877 |
|
![{\displaystyle \log \cos(\lambda -{\text{☊ }})...}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c59fe78680fcc3ad4fe3999e24b97ab983967c16) |
9,9832852
|
![{\displaystyle \log \cos \beta ..........}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aa89314d94bf152f173c19e5972271eb0a63f2fb) |
9,9991289 |
|
|
9,9824141
|
![{\displaystyle \log r'.............}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f2a246912eb3fe325963ca577f62ef3e6b63c461) |
0,3251166 |
|
![{\displaystyle \log \cos u.........}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b28c537850ae1126f66446254b085214802cc525) |
9,9824141
|
Le calcul, d’après les formules III, VII, se ferait de la manière
suivante :
![{\displaystyle \log \sin u.........}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9bd51f51fd3fea4023be3f21a037d1188bf4159f) |
9,4454714![{\displaystyle n}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b) |
|
![{\displaystyle \log \operatorname {tang} {\tfrac {1}{2}}i........}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4df568179dcac02ea3ecb245509a7c1f1ec84018) |
9,0604259
|
![{\displaystyle \log \sin i.........}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0c62429aa1b5b4186db619f57a951d45565a9152) |
9,3557570 |
|
![{\displaystyle \log \operatorname {tang} \beta .........}](https://wikimedia.org/api/rest_v1/media/math/render/svg/34dceb55fb2b3dda2a334d4ec3cca4ac0f5fcf50) |
8,8020995
|
![{\displaystyle \log \sin \beta .........}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e5a89308716c82b35e6ec324b1ec3ca07d600173) |
8,8012284![{\displaystyle n}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b) |
|
![{\displaystyle \log \cos u\,..........}](https://wikimedia.org/api/rest_v1/media/math/render/svg/16b3777a7e61e9d161f97cc1fee03308be9e7b96) |
9,9824141
|
3° 37′ 40,02″n |
|
![{\displaystyle \log \sin(u-\lambda +{\text{☊ }})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ff4e481934a1286da04fcef187462cb285f21c2b) |
7,8449395
|
360° 24′ 03,34″n
|
195° 47′ 40,25″n
|
52
En considérant
et
comme des quantités variables, la différentiation de l’équation III, article 50, donne
![{\displaystyle \operatorname {cotang} \beta \,d\beta =\operatorname {cotang} i\,di+\operatorname {cotang} u\,du}](https://wikimedia.org/api/rest_v1/media/math/render/svg/82eeedd3136a74dd6acca422351feb7b65a1139a)
.
ou
XII.
|
|
|
De même, en différentiant l’équation I, nous obtenons
(XIII)
|
|
|
Enfin, par la différentiation de l’équation XI, il vient
![{\displaystyle dr'=\cos \beta \,dr-r\sin \beta \,d\beta }](https://wikimedia.org/api/rest_v1/media/math/render/svg/ed513e75e9e82f96ea1b3ea29c66804f11fbcf09)
,
ou
![{\displaystyle dr'=\cos \beta \,dr-r\sin \beta \sin(\lambda -{\text{☊ }})\,di-r\sin \beta \sin i\cos(\lambda -{\text{☊ }})\,du}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f7df1d77a0a1426945786dcb507f489118e9660)
.
Dans cette dernière équation les termes qui contiennent
et
doivent être divisés par
ou les autres termes être multipliés