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書籍 Three times the sum of the squares of the sides of a triangle is equal to four times... の書籍検索結果 66 件中 1 - 10 件目
" Three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians. "
A Sequel to the First Six Books of the Elements of Euclid: Containing an ... - 23 ページ
John Casey 著 - 1882 - 158 ページ
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A Collection of Cambridge Mathematical Examination Papers: Papers in the ...

John Martin Frederick Wright - 1831
...of the squares be joined ; the sum of the squares of the sides of the hexagonal figure thus formed is equal to four times the sum of the squares of the sides of the triangle. 14,. If all the angular points of a regular polygon of n sides be joined, and...

The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 390 ページ
...the rectangle is a maximum when the line is bisected. Cor. 4. Since (I. 47. cor. 4.) the difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base, it follows, from the first corollary above,...

A Treatise on Statics: Containing the Theory of the Equilibrium of Forces ...

Samuel Earnshaw - 1845 - 233 ページ
...Consequently, in the case of the triangle (Art. 147), EC- + AC? + AB* = 3. (AGP + BG* + CCP). Hence the sum of the squares of the sides of a triangle is equal to three times the sum of the squares of the distances of its angular points from its centre of gravity....

Mechanics for Practical Men

1845 - 238 ページ
...(a* + J'+c'+^ + S' + S'2), that 18 In any triangular pyramid, the sum of the squares of its six edges is equal to four times the sum of the squares of the distances of the centre of gravity from each angle of the figure. This property of the triangular pyramid...

The first six and the eleventh and twelfth books of Euclid's Elements; with ...

James Thomson - 1845 - 358 ページ
...the rectangle is a maximum when the line is bisected. Cor. 4. Since (I. 47, cor. 4) the difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base, it follows, from the first corollary above,...

Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Robert Potts - 1845
...of the squares be joined ; the sum of the squares of the sides of the hexagonal figure thus formed is equal to four times the sum of the squares of the sides of the triangle. GEOMETRICAL EXERCISES ON BOOK III. THEOREM I. If AB, CD be chords of a circle...

Analytical Geometry: With the Properties of Conic Sections, and an Appendix ...

John Narrien - 1846 - 202 ページ
...proposition it may be proved, that the sum of the squares of the four diagonals of the parallelepiped BN is equal to four times the sum of the squares of the three edges about one of the solid angles ; that is, We have already, as above, the value of OP2. Now...

The Mathematician, 第 2 巻

1847
...with much regret. LXXXVI. By Amicus. In every tetrahedron, the sum of the squares of the six edges is equal to four times the sum of the squares of the lines which join the middles of the opposite edges. [FntST SOLUTION. Mr. JW Elliott, Greatham.~\ Let ABCD...

The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich, Thomas Stephens Davies, Stephen Fenwick, William Rutherford - 1853
...together with double the square on half the base. 8. Three times the sum of the squares on the three sides of a triangle is equal to four times the sum of the squares of the Hues drawn from the angles to bisect the opposite sides. 9. The difference between the squares on two...

The elements of plane and spherical trigonometry

John Hind - 1855
...of the squares be joined : the sum of the squares of the sides of the hexagonal figure thus formed, is equal to four times the sum of the squares of the sides of the triangle. 23. If all the angular points of a regular polygon be joined, and r be the radius...




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