| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...DX will be the fourth proportional required : for since BX is parallel to AC, we have the proportion **DA : DB : : DC : DX ; now the three first terms of...proportional to the three lines A, B, B. PROBLEM III.** Tofind a mean proportional between two given lines A and B. Upon the indefinite line DF, take DE=A,... | |
| John Radford Young - Euclid's Elements - 1827 - 208 pages
...same construction serves for finding a third proportional to two given lines, as A and B ; this being **the same . as a fourth proportional to the three lines A, B, B.** D, PROPOSITION IV. PROBLEM. To divide a given straight line AB into parts proportional to given lines.... | |
| Adrien Marie Legendre - Geometry - 1828 - 346 pages
...BX is parallel to AC, we have the proportion DA : DB : : DC : DX ; now the three first terms of this **proportion are equal to the three given lines ; consequently DX is the fourth proportional required.** 238. Cor. A third proportional to two given lines A, B, may be found in the same manner, for it will... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...BX is parallel to AC, we have the proportion DA : DB : : DC : DX ; now the first three terms of this **proportion are equal to the three given lines : consequently...found in the same manner, for it will be the same as a** fourthproportional to the three lines A, B, B. tv PROBLEM III. To find a mean proportional between... | |
| Adrien Marie Legendre - Geometry - 1839 - 372 pages
...BX is parallel to AC, we have the proportion DA : DB : : DC : DX ; now the first three terms of this **proportion are equal to the three given lines : consequently...fourth proportional to the three lines A, B, B. PROBLEM** IIL To find a mean proportional between two given lines A and B. Upon the indefinite line DF, take... | |
| Nathan Scholfield - 1845 - 896 pages
...since BX is parallel to AC, we have the proportion DA : DB::DC : DX; now the first three terms of this **proportion are equal to the three given lines; consequently...fourth proportional to the three lines A, B, B. PROBLEM** IV. To find a mean proportional between two given lines A and B. Upon the indefinite line DF, take... | |
| Elias Loomis - Conic sections - 1849 - 252 pages
...have D Cor. In the same manner may be found a third proportional to two given lines A and B; for this **will be the same as a fourth proportional to the three lines A,** BB AB : BD : : AC : CE (Prop. XVI., B. IV.). PROBLEM XIX. To find a mean proportional between two given... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...proportion (P, 15, c. 1), DA : DB :: DC : DX; 124 Cor. A third proportional to two given lines, J., .5, **may be found in the same manner, for it will be the...to the three lines, A, B, B. PROBLEM III. To find** & mean proportional between tw» given lines A and B. Upon the indefinite line DP, take DE=^A, and... | |
| Charles Davies - Geometry - 1854 - 436 pages
...to AC, we have the proportion (p. 15, c. 1), DA : DB : : DC : DX; now, the first three terms of this **proportion are equal to the three given lines : consequently, DX is the fourth proportional required.** 124 GEOMETRY. Cor. A third proportional to two given lines, A, B, may be found in the same manner,... | |
| Elias Loomis - Conic sections - 1858 - 256 pages
...IV.). Cor. In the same manner may be found a third proportional to two given lines A and B ; for this **will be the same as a fourth proportional to the three lines A,** BB D PROBLEM XIX. To find a mean proportional between two given lines. Let AB, BC be the two given... | |
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