## Plane and Solid Geometry |

### From inside the book

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**intersect**in one point only . 96 COROLLARY 3. Two points determine a straight line . POSTULATES 97 Postulates , like axioms , are numerous . Euclid calls a postulate " a request , " and adds , " To my postulates I request , to my axioms ... Page 18

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**intersecting**lines ; as , a and b ; also , c and d . EXERCISES axb a 1 Find the complement of an angle of 27 ° . 2 Find the supplement of an angle of 27 ° . 3 Of what angle is 58 ° the complement ? 4 Of what angle is 126 ° the ... Page 19

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**intersecting**lines . CONCLUSION . ≤ m = ≤ n , and ≤ s = Lt. PROOF Zm is the sup . of ≤ s , and n is the sup . of s . :: < m = Ln . § 103 " The supplements of equal are equal . " § 105 Q. E. D. Likewise s = Lt. EXERCISES 17 If ≤1 ... Page 23

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**intersects**two or more straight L lines . Thus , the line T is a transversal to the lines L and L ' , and the eight angles formed at the points of intersec- L tion are named as follows : 8 / h Post . 2 § 117 $ 115 Q. E. D. a / b c / d T ... Page 28

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**intersect**at K. Then m = = Ls , Ls . and .. n < m = Ln . But n = Lo . .. m , n , and o are equal . Again , n + p = 2 rt . 4 . ≤ Z Substituting m for its equal ≤ n , we have m + ≤ p = 2 rt .. § 122 § 122 Ax . 11 § 112 § 103 Q. E. D. ...### Contents

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### Common terms and phrases

ABCD altitude angles are equal arc BC assigned quantity base bisectors bisects chord circumference circumscribed circle CONCLUSION cone construct COROLLARY cylinder diagonals diameter diedral angles divided equiangular equiangular polygon equidistant equilateral triangle exterior angle Find the area Find the locus Find the ratio frustum given circle given line given point homologous sides hypotenuse HYPOTHESIS inches inscribed intersecting isosceles trapezoid isosceles triangle lateral area legs line of centers mean proportional median mid-points number of sides parallelogram parallelopiped perimeter perpendicular polyedral angle polyedron prism PROOF Draw Prove pyramid Q. E. D. EXERCISES Q. E. D. PROPOSITION quadrilateral radii radius rectangle regular polygon rhombus right angles right triangle SCHOLIUM secant segments similar triangles slant height SOLUTION sphere spherical polygon spherical triangle straight line surface tangent THEOREM trapezoid triangle ABC triedral vertex volume

### Popular passages

Page 168 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.

Page 41 - In an isosceles triangle the angles opposite the equal sides are equal.

Page 38 - ... greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 35 - Any side of a triangle is less than the sum of the other two sides...

Page 242 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.

Page 174 - In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector.

Page 172 - If from a point without a circle a tangent and a secant are drawn, the tangent is the mean proportional between the whole secant and its external segment.

Page 171 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.

Page 192 - The areas of two rectangles having equal altitudes are to each other as their bases.

Page 65 - The perpendicular bisectors of the sides of a triangle meet in a point. 12. The bisectors of the angles of a triangle meet in a point. 13. The tangents to a circle from an external point are equal. 14...