 | 1842 - 108 strani
...a, BQ —t, we have OB =: a + b, OD = a + b — r,, PD =: a + r,, and OP = b. Hence, by the ordinary formula for the area of a triangle in terms of its sides, we derive ( ДВРО)' = (a -(- i) a (b — rn) r,. But ДВРО = £ DF . PO, and by a property of... | |
 | Henry Burchard Fine - 1890 - 154 strani
...commentary of Theon of Alexandria (380 AD) on Ptolemy's * The formula Vs (s — o) (s — 6) (s — c) for the area of a triangle in terms of its sides is due to Hero. t Many attempts have ftbeen made to discover the methods of approximation used by Archimedes... | |
 | Florian Cajori - 1893 - 476 strani
...Elements. 2' Some of Heron's formulas point to an old Egyptian origin. Thus, besides the above exact formula for the area of a triangle in terms of its sides, Heron gives the formula q 'y a * x -, which bears a striking likeness to the for2 2i nrala ?' + "2... | |
 | Florian Cajori - 1898 - 512 strani
...Elements.^ Some of Heron's formulas point to an old Egyptian origin. Thus, besides the above exact formula for the area of a triangle in terms of its sides, Heron gives the formula ttl "J" aa x -, which bears a striking likeness to the for£i £ mula a' T"... | |
 | Fletcher Durell - 1904 - 232 strani
...squares of their radii, or of their diameters. In the writings of Hero (Alexandria, 125 BC) we first find the formula for the area of a triangle in terms of its sides, K=Vs(s — a) (s — b) (s — c). Hero also was the first to place land-surveying on a scientific... | |
 | Fletcher Durell - 1911 - 553 strani
...squares of their radii, or of their diameters. In the writings of Hero (Alexandria, 125 BC) we first find the formula for the area of a triangle in terms of its sides, K= V s(s — a) (s—b) (s — c) . Hero also was the first to place land-surveying on a scientific... | |
 | Fletcher Durell - 1904 - 382 strani
...of their radii, or of their diameters. In the writings of Hero (Alexandria, 125 B. 0.) we first find the formula for the area of a triangle in terms of its . sides, K=VS(R — a) (s — 6) (s — c). Hero also was the first to place land-surveying on a scientific... | |
 | 1921 - 970 strani
...Jf'+zz)/2. * PROBLEMS FOR SOLUTION. 706. Proposed by numerous contributors. Is there any simple proof of the formula for the area of a triangle in terms of its sides which does not involve trigonometry nor any complicated algebraic manipulations? 707. Proposed by Daniel... | |
 | Edward Rutledge Robbins - 1906 - 268 strani
...n mm m m Qn nn m n n C mn -FT" nn n nn «in mn mn nn m 1 n 3 201 FORMULAS 397. PROBLEM. To derive a formula for the area of a triangle in terms of its sides. Given : A ABC, having sides = a, 6, e. Required : To derive a formula for its area, containing only... | |
 | Edward Rutledge Robbins - 1907 - 428 strani
...whole line. 200 C mn nr n „.„ HH. n mn n m | m.ti 3 n n BOOK IV FORMULAS 397. PROBLEM. To derive a formula for the area of a triangle in terms of its sides. Given : A ABC, having sides = a, 6, c. Required: To derive a formula for its area, containing only... | |
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Heron to prove his formula for the area of a triangle in terms of its sides, is... 
