 | Benjamin Theophilus Moore - Measurement - 1863 - 320 pages
...area of a rectangle. In Euclid's Elements of Geometry, Book VI. Proposition 23, it is proved that " Equiangular parallelograms have to one another the...ratio which is compounded of the ratios of their sides ;" and therefore rectangles, which are equiangular parallelograms, have to one another this same ratio.... | |
 | William Walton - Mathematics - 1864 - 234 pages
...sideAB = CD = EF=...= ZA = BC=..., the number of sides being odd. So that all the sides are equal. 5. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. If one parallelogram have to another parallelogram the ratio which is compounded of the ratios of their... | |
 | University of Cambridge - 1864 - 694 pages
...its angular points on the same circle and all its angles equal, then shall all its sides be equal. 5. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. If one parallelogram have to another parallelogram the ratio which is compounded of the ratios of their... | |
 | Euclides - 1864 - 448 pages
...parallelograms are proportional to the squares of their homologous sides. 36. How is it shewn that equiangular parallelograms have to one another the ratio which is compounded of the ratios of their bases and altitudes ? 37. To find two lines which shall have to each other, the ratio compounded of... | |
 | Euclides - 1865 - 402 pages
...is to CD, as EF to OH. (T. 7.) If, therefore, four straight lines, &c. QED PROP. XXIII.— THEOREM. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides, (References— Prop. i. U ; v. 11, 22, def. A ; VI. 1, 12.) Let AC, CF be eqniangolar parallelograms,... | |
 | Robert Potts - 1865 - 528 pages
...parallelograms, are proportional to the squares on their homologous sides. 36. How is it shewn that equiangular parallelograms have to one another the ratio which is compounded of the ratios of their bases and altitudes ? 37. To find two lines which shall have to each other, the ratio compounded of... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...hava the following theorem, triangles which, ham one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of their sides. Then VI. 19 is an immediate consequence of this theorem. For let ABC and DEF be similar triangles,... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...straight lines &c. QED PROPOSITION 23. THEOREM. Parallelograms which are equiangular to one another have to one another the ratio which is compounded of the ratios of their sides. Let the parallelrgram AC be equiangular to the parallelogram CF, having the angle BCD equal to the... | |
 | Euclid - 1868 - 138 pages
...Та laoyúvia я-apaXX1)Xóуpa/1/ш irpоc a\\rf\a \oyov ?^fi TÔv avyKfifiivov ÍK TÜV ir\evpwv. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. Statement Let AC and CF be equiangular parallelograms, having the angle BCD equal to the angle ECG.... | |
 | Robert Potts - 1868 - 434 pages
...parallelograms are proportional to the squares of their homologous sides. 36. How is it shewn that equiangular parallelograms have to one another the ratio which is compounded of the ratios of their bases and altitudes r 37. To find two lines which shall have to each other, the ratio compounded of... | |
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Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. 
