# The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth : the Errors by which Theon, Or Others, Have Long Ago Vitiated These Books are Corrected, and Some of Euclid's Demonstrations are Restored : Also, the Book of Euclid's Data, in Like Manner Corrected : to this Edition are Also Annexed, Elements of Plane and Spherical Trigonometry (Google eBook)

Robert Desilver, 1821 - Mathematics, Greek - 516 pages

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### Contents

 Section 1 i Section 2 iii Section 3 7 Section 4 9 Section 5 49 Section 6 88 Section 7 100 Section 8 117
 Section 16 250 Section 17 261 Section 18 271 Section 19 272 Section 20 274 Section 21 276 Section 22 283 Section 23 285

 Section 9 153 Section 10 190 Section 11 191 Section 12 194 Section 13 224 Section 14 230 Section 15 240
 Section 24 286 Section 25 290 Section 26 293 Section 27 295 Section 28 365 Section 29 461 Section 30 491

### Popular passages

Page 11 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 155 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Page 329 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Page 20 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Page 9 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Page 55 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 53 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Page 318 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Page 21 - The angles which one straight line makes with another upon one tide of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.
Page 27 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.