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Books Books 1 - 10 of 41 on It will be sufficient to lay the edge of a rule on C, so as to be parallel to a line....  
" It will be sufficient to lay the edge of a rule on C, so as to be parallel to a line supposed to pass through B and D, and to mark the point of intersection G. 126. If after a field has been surveyed, and the area computed, the chain is found to be too... "
A practical application of the principles of geometry to the mensuration of ... - Page 71
by Jeremiah Day - 1815 - 96 pages
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Elements of geometry: containing the first six books of Euclid, with a ...

John Playfair - Trigonometry - 1806 - 311 pages
...is the same with the duplicate ratio of their sides ; and hence, also, any two similar rectilineal figures are to each other as the squares of their homologous sides. PROP. XXI. THEOR. Book VI. RECTILINEAL figures, which are similar to the same rectilineal figure, are...
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The complete measurer: or, The whole art of measuring, containing the ...

Thomas Keith, William Hawney - 1817
...I = 7- X VD d 3/ \D d 3/ a d 3 the solidity of the frustum ABD c. Now all similar plane figures are to each other as the squares of their homologous sides. Therefore A 1 a : : D* : d* or = , put each off these equal to m ; then A * D* and a ...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 pages
...polygon, we shall have S' =p'2? : (A, B, A' B', &c.) Hence S : S': :p2 :p's ; hence the surfaces of similar figures are to each other as the squares of their homologous sides. Let us now proceed to polyedrons. We may take it for granted, that a face is determined by means of...
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The second [-fifth and sixth] part of A course of Mathematics: adapted to ...

Jeremiah Day, Matthew Rice Dutton - Geometry - 1824
...original figure. The area of the triangle may then be found by multiplying its base into half its height ; and this will be the contents of the field. In practice...other as the squares of their homologous sides. (Euc. 20.6.) The proportion may be stated thus ; As the square of the true chain, to the square of that by...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 324 pages
...polygon, we shall have S' = ^/i0 : (A, B, A', B', &c.) Hence S : S' : : p2 : p'1 ; hence the surfaces of similar figures are to each other as the squares of their homologous sides. Let us now proceed to polyedrons. We may take it for granted, that a face is determined by means of...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 129 pages
...ABCDE:FGHIK::ABC:FGH. But ABC : FGH : : AB* : p G*. Therefore ABCDE : FGHIK : : AB* : FG*. In other words, similar figures are to each other as the squares of their homologous sides. 117. THEOREM. Circles are to each other as the squares of their radii. No diagram is necessary...
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Elements of geometry: Being chiefly a selection from Playfair's geometry

Francis Nichols - Mathematics - 1829 - 186 pages
...other is the same with the duplicate ratio of their sides; and hence, also, any two similar rectilineal figures are to each other as the squares of their homologous sides. CoR. 3. Two similar triangles, or two similar polygons, are to each other as any rectilineal figure...
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A Treatise of Plane Trigonometry: To which is Prefixed a Summary View of the ...

Jeremiah Day - Logarithms - 1831 - 155 pages
...original figure. The area of the triangle may then be found by multiplying its base into half its height ; and this will be the contents of the field. In practice,...the area of a field measured by a chain 66.4 feet long, be computed to be 32.6036 acres ; what is the area as measured by the true chain 66 feet long...
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The principles of plane trigonometry, mensuration, navigation and surveying ...

Jeremiah Day - Measurement - 1831
...original figure. The area of the triangle may then be found by multiplying its base into half its height ; and this will be the contents of the field. In practice,...the area of a field measured by a chain 66.4 feet long, be computed to be 32.6036 acres ; what is the area as measured by the true chain 66 feet long...
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A new and easy introduction to the mathematics: containing. A system of ...

Arithmetic - 1831 - 396 pages
...the polygon ; then multiply that square by the multiplier set against the name *This rule depends on the principle, that similar figures are to each other as the squares oftluir llke sides. The multipllers in the table are the areas of the respective figures to the side...
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