 | 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
...Enclid, though it is clear that a technical use of the term was intended in the enunciation of Prop. 23, Book vi. : " Equiangular parallelograms have to one...which is compounded of the ratios of their sides." It may easily be seen that the ratio of two equiangular parallelograms is in some way dependent on... | |
 | 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... | |
 | Civil service - 1866 - 270 pages
...extremities of the base have the same ratio which the other sides of the triangle have to one another. 7. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. 8. Trisect a given straight line. 9. Construct a rectangle which shall be equal to a given square (1)... | |
 | 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
...the following theorem, triangles which have one angle of tJie 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. ig is an immediate consequence of this theorem. For let ABC and DEF be similar triangles,... | |
 | 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... | |
 | Woolwich roy. military acad - 1868 - 426 pages
...circles in E and F respectively, show that if AB produced meet EF in C then EC is equal to FO. 11. Equiangular parallelograms have to one another the ratio which is compounded of the ratio of their sides. Assuming that the area of a triangle may be represented by half the product of... | |
| |
Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF... 
