# The Elements of geometry [Euclid book 1-3] in general terms, with notes &c. &c. Also a variety of problems & theorems. [Ed. by J. Luby. With] The elements of plane geometry, comprising the definitions of the fifth book, and the sixth book in general terms, with notes [&c.] by J. Luby [described as] Pt. 3

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### Contents

 Section 1 iv Section 2 v Section 3 7 Section 4 33 Section 5 41 Section 6 44 Section 7 77 Section 8 97
 Section 9 117 Section 10 151 Section 11 1 Section 12 3 Section 13 10 Section 14 44 Section 15 47 Section 16

### Popular passages

Page 100 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 11 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Page 130 - The angle at the centre of a circle is double the angle at the circumference on the same arc.
Page 135 - ... a circle. The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle. The opposite angles of any quadrilateral inscribed in a circle are supplementary ; and the converse.
Page 32 - ... polygons are to each other in the duplicate ratio of their homologous sides.
Page 37 - In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the sum of the squares described on the sides which contain the right angle.
Page 124 - If from a point within a circle more than two equal straight lines can be drawn to the circumference, that point is the centre of the circle.
Page 6 - Convertendo ; when it is concluded, that, if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth.
Page 10 - If two triangles have two sides of the one equal to two sides of the other, each to each, and" have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to the angle contained by the two sides equal to them, of the other. Let ABC, DEF be two triangles, having the two sides AB, AC, equal to the two sides DE, DF, each to each, viz.
Page 118 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.