## Plane and Solid Geometry |

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Page 140

Isaac Newton Failor. as , BOOK III PROPORTION AND SIMILAR POLYGONS DEFINITIONS 317 A proportion is an equality of ...

Isaac Newton Failor. as , BOOK III PROPORTION AND SIMILAR POLYGONS DEFINITIONS 317 A proportion is an equality of ...

**mean proportional**between a and c . 326 A continued proportion is a series of equal ratios ; as , a : b c : de : f ... Page 141

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**mean proportional**between two quantities is equal to the square root of their product . HYPOTHESIS . CONCLUSION . a : bb : c . b = Vac . PROOF b2 = ac ... proportional between m and n . THEORY OF PROPORTION 141 THEORY OF PROPORTION • Page 142

Isaac Newton Failor. 572 Find the

Isaac Newton Failor. 572 Find the

**mean proportional**between m and n . 573 Find the third proportional to 2 and 6 . 574 Find the third proportional to m and n . PROPOSITION III . THEOREM 330 If the product of two quantities is equal to ... Page 160

... proportional to 24 , 20 , 34 . 626 Find the third proportional to 15 and 45 . 627 Find the

... proportional to 24 , 20 , 34 . 626 Find the third proportional to 15 and 45 . 627 Find the

**mean proportional**between 4 and 121 . 628 In a triangle ABC , DE is parallel to BC . If AD : DB = 3 : 2 , and BC = 15 , find DE . 629 In a ... Page 164

... proportional between the segments of the hypotenuse . 3 Each leg of the right triangle is the mean pro- portional ...

... proportional between the segments of the hypotenuse . 3 Each leg of the right triangle is the mean pro- portional ...

**mean proportional**between BD and DC . PROOF In the similar △ BDA and ADC , BD : AD = AD : DC . § 349 3 BA is the ...### 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...