### Contents

 Section 1 14 Section 2 15 Section 3 26 Section 4 59 Section 5 75 Section 6 106 Section 7 107 Section 8 122
 Section 12 155 Section 13 161 Section 14 165 Section 15 166 Section 16 167 Section 17 173 Section 18 206 Section 19 225

 Section 9 128 Section 10 129 Section 11 148
 Section 20 238 Section 21 98

### Popular passages

Page 32 - 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.
Page 199 - ... that triangles on the same base and between the same parallels are equal...
Page 94 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 23 - Four quantities are said to be in proportion when the product of the extremes is equal to that of the means : thus if A multiplied by D, be equal to B multiplied by C, then A is said to be to B as C is to D.
Page 95 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 37 - ABDE+ACGF the sum of the squares —BKLH-\-KCML, the sum of the two parallelograms or square BCMH; therefore the sum of the squares on AB and AC is equal to the square on BC.
Page 24 - Things that are equal to one and the same thing, are equal to each other. 2. Every whole is greater than its part. % 3. Every whole is equal to all its parts taken together. 4 If to equal things, equal things be added, the whole will be equal. 5. If from equal things, equal things be deducted the remainders will be equal.
Page 36 - XIII. •All parallelograms on the same or equal bases and between the same parallels...
Page 182 - VI. To find the content of a triangular piece of ground, Multiply the base by half the perpendicular, or the perpendicular by half the base ; or take half the product of the base into the perpendicular. The reason hereof is plain, from cor.
Page 35 - Triangles upon equal bases, and between the same parallels, are equal to one another.