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" And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB... "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Σελίδα 30
των Euclid - 1835 - 513 σελίδες
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Report of Her Majesty's Civil Service Commissioners: Together with ..., Τόμος 20

1876 - 586 σελίδες
...greater base shall be greater than the angle contained by the sides equal to them, of the other. 2. The opposite sides and angles of a parallelogram are equal to one The longer side of a parallelogram is double of the shorter. INDIA» О. В. Prove that the straight...

Solutions to the mathematical examination papers set for admission to the ...

D. Tierney - 1877 - 126 σελίδες
...their other angles shall be equal, each to each, viz. those to which the equal sides are opposite. 2. The opposite sides and angles of a parallelogram are equal to one another, and the diameter bisects it, that is, divides it into two equal parts. From the angle A of the parallelogram...

Elements of geometry, based on Euclid, book i

Edward Atkins - 1877 - 72 σελίδες
...it was shown to be equal to it. Therefore, the straight lines, &c. QED Proposition. 34. — Theorem. The opposite sides and angles of a parallelogram are equal to one another, and the diagonal bisects the parallelogram — tluit is, divides it into two equal parts. Let ACDB...

Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1877 - 458 σελίδες
...angle ABC is equal to the whole angle ADC. But the angle BAD has been proved equal to the angle BCD ; therefore the opposite sides and angles of a parallelogram are equal to each other. Oor.l. Two parallels, AB, CD, comprehended between two other parallels, AD, BC, are equal...

The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878 - 100 σελίδες
...equal (Ax. 2) to the whole angle ADC. And the angle BAD has 1been proved to be equal to the angle BCD. Therefore the opposite sides and angles of a parallelogram are equal to one another. Also the diagonal BD bisects the parallelogram AC, because the two triangles ABD, BCD, are equal. Similarly...

Complete guide to the certificate and scholarship examinations, by a head ...

J T. Amner - 1878 - 226 σελίδες
...; what other condition is required that the triangles may be equal in all respects ? Section 2. 1. The opposite sides and angles of a parallelogram are equal to one another. If the four corners of a square piece of paper are folded to meet in the centre of the square, another...

Report of Her Majesty's Civil Service Commissioners: Together with ..., Τόμος 22

1878 - 632 σελίδες
...their other angles shall be equal, each to each, viz., those to which the equ«l sides are opposite. 2. The opposite sides and angles of a parallelogram are equal to one another, and the diameter bisects the parallelogram, that is. divides it into two equal parts. From the angle...

Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879 - 94 σελίδες
...bisecting lines, a line be drawn to the opposite angle of the triangle, it will bisect that angle. 2. The opposite sides and angles of a parallelogram are equal to one another, and the diameter bisects it, that is divides it into two equal parts. Prove further that, if from any...

Moffatt's pupil teachers' course (ed. by T. Page). Candidates, 2nd (-4th) year

Moffatt and Paige - 1879 - 474 σελίδες
...B D. Therefore, the straight lines which join the extremities, etc. QED Proposition XXXIV. Theorem. The opposite sides and angles of a parallelogram are equal to one another, and the diameter bisects it, that is, divides it into two equal parts. Let ACDB be a parallelogram,...

Papers for teachers

1880 - 594 σελίδες
...farms, must have resembled the most flourishing parts of Lombardy or the Netherlands." Euclid. — i. The opposite sides and angles of a parallelogram are equal to one another, and the diameter bisects it, that is, divides it into two equal parts. Two parallel lines cut a series...




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