 | Thomas Simpson - Calculus - 1750 - 604 pages
...i. PRO B. VII. 431. Three Points A, B, C being given, to find the Pojition of a fourth Point P, fo that, if Lines be drawn • from thence to the three former ; the Sum of the Produtts tfXAP, JXBP, and rXCP (where a, b and c deaott given Numbers) Jball be a Minimum. F... | |
 | Thomas Simpson - Calculus - 1776 - 598 pages
...9. PROB. VII. 431. Three Points А, В, С being given, to find the Poßtion of a fourth Point P, fo that, if Lines be drawn from thence to the three former, the Sum of the Producís a X AP, b X BP, and с xCP (ivbere a, b and с denote given Numbers) jhall be a Minimum.... | |
 | Thomas Simpson - Calculus - 1823 - 392 pages
...to each other in the ratio o/ 4 io 9. PROBLEM VII. 481. Three Points А, В, С being given, to ßnd the Position of a fourth Point P, so that, if Lines be drawn from thence to the three forme?, the Sum of the Products à x АР, Ъ x BP, and с х С P (where а, Ъ and с denote given... | |
 | Electronic journals - 1920 - 514 pages
...more general problem: Three points A, B, and C being given, to find the position of a fourth point V, so that if lines be drawn from thence to the three former, the sum a-AP + b-BP + c-CP, where a, b, c denote given numbers, shall be a minimum. The further history of... | |
 | Edinburgh Mathematical Society - Electronic journals - 1897 - 208 pages
...closely connected with the problem To find that point the sum of whose distances from the vertices oj a triangle is a minimum. This problem, Viviani relates,...thence to the three former, the sum a . AP + b . BP + c . CP where abc denote given numbers, shall be a minimum. Both the particular and the more general... | |
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If CP and BP be produced to E and F, it will appear from Art. 35. and 36. that the Sine of BPE muft be to that of APE, as a to b; and the Sine of CPF (BPE) to that of APF, as a to r. 