pieds

N. B.—Lorsque dans la division d’une hauteur par la base, le quotient donne un reste après la troisième décimale et que .‘on demande berucoup d’exactitude.

Prenez la longueur pour les trois premiers chiffres ; soustrayez-la de la longueur suivante ; multipliez le reste par le reste fractionnaire, ajoutez le produit à la première longneur, et ia somme sera

la longueur pour le quotient total.

ExemPzr.— Quelle est la iongueur d’un are ée cerele, dont la base est 35 piedset la hauteur ou

sinus-verse 8 pieds ?

8-85 — .2985714 ; la lougueur tabulaire pour .228—.1.13331, etpour 29—1.13444; la différence entre ces longueurs est .00113. Alors .5714 x .00115—(16,45682. De là .228—1.13331 .0005714—.000645682

et 1,1339586582, la somme par la

quelle il faut

multiplier la base de l'arc; et 1.133556. Y35=30.68845 pieds.

TAXSIIC V'AX.

TABLE DES LONGUEURS DES ARCS DE DEMI-TLLIPSES. Le grand axe étant À ct divisé ex; 1000 parties égales.

Haut. Long. |! Hant.| Long, || ant. Long, Haut.| Long. | Hant. | Lons. .l 1.04162 |! .14S8 | 1.091119 !!,196 | 1.14531 .244 | 1.2038 || .292 | 1.26601 101 ! 1.041262 [| .149 | 1.09228 |!.197 | 1.14646 | 245 | 1.20506 || .293 | 1.26734 | 4102 | 1.043562 || .L5 1.0933 198 | 114762 11.246 | 1.20632 || 294 | 1.268567 11,103 ! 1.04462 |! .151 10944 11.199 | 1.148388 || .247 | 1.20758 |.295 1.27 104 ! 1.014562 |.152 1,09558 !!.2 115014 |! .218 | 120884 11.296 | 1.271338 105 | 1.014662 |!.153 | 1.09669 |! .201 | 1.15131 |! .249 | 1.2101 11.297 | 1.27267 C6 | 1.014762 ||.154 | 1.0978 |! .202 | 1.15248 | .25 1.21136 || .298 | 1.27401 .107 | 1.04862 ||.155 | 1.09891 |!.203 | 1.15366 11.251 | 1.21263 || .299 | 1.297535 108 !: 1.014962 !|.156 | 110002 |!.204 | 1.15484 || .252 | 1.2139 || .3 1.27669 109 | 1.05063 |!.157 | 1:10113 || .205 | 1.15602 || .253 | 1.21517 |. 30 1.27803 11 1.051164 ||.1593 ! 1.10224 || .206 | 1.1572 254 | 1.216414 || .302 | 1.27937 JL | 1.052 5 | .19 1.103535 11.207 |! 1.15838 || .255 | 1.21772 || .503 1.28071 112 | 1.05366 || .16 1.104417 203 | 1.15957 256 | 1.2'9 11.304 | 1.28205 113 | 1.05467 |!.16L | 1.1056 1}.209 | 1.16076 1! .257 } 1.22028 || .305 | 1.238339 JH14 ! 1.05568 [11.162 | 1.10672 || .21 1.16196 || .258 | 1.22156 || .306 | 1.28474 115 | 1.056669 |! .163 | 1,10784 || .211 | 1.16316 || .259 | 1.22284 | .307 | 1.28609 116 | 1.0577 154 | 1,10896 !!.212 | 1.16436 || .26 1.22412 |! .308 | 1.28744 JET | 105872 ||.165 | 1.11008 11.213 | 1.16557 1.261 | 1.225141 |! .309 | 1.28879 118 | 1.05974 ||,166 | 1,1112 214 | 1.16678 || .262 | 1.2267 .3l 1.29014 119 | 1.06076 167 | 1.11232 ||.215 | 1.16799 || .263 | 1.22799 || .311 | 1.29149 | 12 1.06178 |!.168 | 1,11344 !!.216 | 1.1692 .264 | 1.22928 || .312 | 1.29285 121 | 1.0628 ||.169 | 1.11456 || .217 | 1.17041 265 | 1.23057 |! .315 | 1.29421 | 122 | 1.06382 || .17 1.11569 || .218 | 1.17163 || .266 | 1.23186 |.314 1.29557 123 | 1.06484 || .17L | 1.11682 || .219 | 1.17285 || .267 | 1.23315 || .315 | 1.29603 124 | 1.06586 |! ,172 | 1,11795 || .22 1.174067 11.268 | 1.23445 || .316 | 1.29829 125 | 1.06689 |!.173 | 1,11908 |! .221 | 1.17529 [1.269 | 1.235795 || .317 | 1.29965 126 | 1.06792 || .174 | 112021 |! .222 | L.17651 .27 1.23705 | .318 | 1.30102 127 | 1.06895 || .175 | 1,19134 || .223 | 1.17774 || .271 | 1.233838 || .319 | 1.30239 128 | 1.06998 || .176 | 1,12247 || .224 | 1.17897 || .272 | 1.23966 || .32 1.30376 129 | 1.07001 177 | 11236 .225 | 1.1802 | 2173 | 1.24097 |!.321 | 1.30513 13 1.07204 |! .178 | 1.12473 || .226 | 1.18143 || .274 | 1.24228 || .322 | 1.3065 131 | 1.073508 |! ,179 | 1.12586 || .227 | 1.18266 || .275 | 1.24359 | ‘203 | 1.30787 132 | 1.07412 || .18 112699 | .228 | 1.1839 .216 |! 1.2448 || .324 | 1.30924 133 | 1.07516 || .181 | 1.12813 || .229 | 1.18514 || .277 | 1.24612 || .325 | 1.3:061 134 | 1.07621 182 | 1.12927 || .23 1.18638 |! .278 | 1.24744 | .326 | 1.31198 135 | 1.07726 !| .193 ! 1.13041 231 | 1.18762 || .279 | 1.24876 || .327 | 1.31335 136 | 1.07831 |! .184 | 1,13155 || ,232 | 1,18886 || .28 1.2501 11.328 | 1.381472 137 1 1.079357 ||.185 | 1,13269 || .233 1.1901 .281 | 1.25142 || .329 | 1.5161 138 | 1.038043 || .186 | 1.13383 || .234 | 1,19134 || .282 | 1.2527 .33 1.351748 139 | 1.638149 || 187 | 1.13497 || .235 | 1.19258 283 | 1.254106 ||,331 | 1.351886 .l4 1.08255 || .i88 | 1.135611 .236 | 1,19382 || .284 | 1.2553 .332 ! 1.32024 141 ! 1.08362 | 189 | 1.13726 || .237 | 119506 || .285 | 1.2567 335 | 1.321062 142 | 1.089469 |! .19 1.132841 || .238 | L,1963 286 | 1.25803 || .334 | 1,323 143 | 1.038576 191 | 113956 || .238: | 1.19755 || .287 | 1.25936 || .335 | 1.822438 | 144 | 1.08684 192 | 114071 .24 1,1988 .288 | 1.26069 |! 336 | 1.32576 145 | J.08792 193 | 1.14186 || 241 | 1.260005 |! ,289 | 1.26202 || .337 | 1.327165 : 146 | L.08901 194 ! 1,14301 .242 | 1.2012 .29 1.263539 ||.338 | 1.352854 | 147 | 1.0901 195 | 1.144116 243 | 1.299255 || .291 | 1.264608 || .339 | 1.32993