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THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... - Page 106
by Thomas Perronet Thompson - 1833 - 150 pages

## The text of Euclid's geometry, book 1, uniformly and systematically arranged ...

Euclides - 1884 - 214 pages
...are equal to four right angles. Ax. 3. PROPOSITION XXXIII. THEOREM. The straight lines which join the extremities of two equal and parallel straight lines towards the same parts, are also themselves equal and parallel. . GIVEN that AB and CD are equal and parallel, and joined towards...

## The Practical Teacher, Volume 3

Education - 1884 - 708 pages
...angle, and AB is a given side. Л BCA is the triangle required. QEF 2. The straight lines which join the extremities of two equal and parallel straight lines towards the same parts, are also themselves equal and parallel. Prop. 33, Bk. I. 3. The complements of the parallelograms, which...

## Calendar of Dalhousie College and University

Dalhousie University - 1887 - 206 pages
...the angle contained by the sides equal to them, of the other. 8. The straight lines which join the extremities of two equal and parallel straight lines towards the same parts, are also themselves equal and parallel. 9. If a straight line !>e divided into two equal parts and also...

## Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889 - 354 pages
...other. Shew also that the two triangles are equal in all respects. 3. The straight lines which join the extremities of two equal and parallel straight lines...the same parts are themselves equal and parallel. Shew also that the straight lines which join the extremities towards opposite parts, bisect each other....

## Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 442 pages
...CBA + ACB = ACD + ACB, = two rt. As. Proposition 33. THEOREM — The straight lines which join the extremities of two equal and parallel straight lines,...parts, are themselves equal and parallel. Let AB, CD be equal and || st. lines ; AC, BD their joins towards the same parts. Join BC. Then in A8 ABC, DCS, we...

## The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...angles of regular figures use Cor. II.) PROPOSITION 33. THEOREM. The straight lines which join the extremities of two equal and parallel straight lines...same parts are themselves equal and parallel. Let AB and CD be equal and parallel st. lines, and let them be joined towards the same parts by the st. lines...

## Rider Papers on Euclid: Books i and Ii, Graduated and Arranged in Order of ...

Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...angles of every triangle are together equal to two right angles. 33. The straight lines which join the extremities of two equal and parallel straight lines...the same parts are themselves equal and parallel. 34. The opposite sides and angles of a parallelogram are equal to one another, and the diameter bisects...

## The Educational Record of the Province of Quebec: The Medium ..., Volume 11

Education - 1891 - 442 pages
...each of the remainder to gain 10 per cent on the whole 1 Geometry. 1. The straight lines joining the extremities of two equal and parallel straight lines...the same parts, are themselves equal and parallel. State the converse of this proposition. 2. Describe a parallelogram equal to a given rectilineal figure,...

## A Text-book of Geometrical Deductions: Book I [-II] Corresponding to ..., Book 1

James Andrew Blaikie, William Thomson - Geometry - 1891 - 154 pages
...rectilineal figure are together equal to four right angles. 33. The straight lines which join the ends of two equal and parallel straight lines; towards the same parts are themselves equal and parallel. 34. The opposite sides and opposite angles of a parallelogram are equal, and either diagonal bisects...

## The Foundations of Geometry

Edward Travers Dixon - Geometry - 1891 - 180 pages
...Euclid, it is usual to commence by proving Euclid's proposition that 'the straight lines which join equal and parallel straight lines towards the same parts are themselves equal and parallel,' by it ; the above equation being in fact merely Euclid's proposition in vector language. It will be...