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" Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. "
Elements of Geometry: Containing the First Six Books of Euclid with a ... - Strona 140
autor: John Playfair - 1855 - Liczba stron: 318
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - Liczba stron: 410
...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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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1868
...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...
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The Oxford, Cambridge, and Dublin Messenger of Mathematics, Tom 4

1868
...points a, /3. The areas of triangles which have 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 the sides. Applying this to the triangles PAB, Pa/8, which have the angle at P common, we have algebraically...
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Civil service guide

Robert Johnston (F.R.G.S.) - 1869 - Liczba stron: 178
...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)...
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The Edinburgh university calendar

Edinburgh univ - 1871
...angular points of the triangle, the greatest of these shall be equal to the other two together. 6. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. 8. If the angle of a triangle be bisected, and perpendiculars be drawn to the bisecting line from the...
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Dublin examination papers

Dublin city, univ - 1871
...triangles will be equiangular, and will have those angles equal about which the sides are proportional ? 8. Equiangular parallelograms have to one another the ratio which is compounded of the ratio of their sides ? DR. STUBBS. 1. The square of the bisector of the vertical angle of a triangle...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - Liczba stron: 349
...are together equal to four times the quadrilateral figure. PROPOSITION XXVI. THEOREM. (Eucl. vi. 23.) Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. B. JI \ \. K. ZM Let AC and CF be equiangular Os, baving L BCD = L ECG. Then must LJ AC have to EH...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...is to CD, as EF to GH (V. 7). If therefore, four straight lines, &c. QED PROPOSITION 23. —Theorem. Equiangular parallelograms have to one another the...parallelograms, having the angle BCD equal to the angle ECG. Then the ratio of the parallelogram AC to the parallelogram CF, shall be the same with the ratio which...
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Five Years in an English University

Charles Astor Bristed - 1874 - Liczba stron: 572
...of gravity. SENATE-HOUSE EXAMINATION. FRIDAY, Jan. 3, 1845. 9 . . . ll£. 1. DEFINE compound ratio. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. 2. Draw a straight line perpendicular to a plane from a given point above it. a. Show how to find the...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...the other, have the sides ahout the equal angles reciprocally proportional. Cor. 3. — Hence also equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. Schol. — If an oblique-angled parallelogram be taken, and the same construction made as in I. App.,...
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