## Elements of Geometry: Plane and Solid |

### From inside the book

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**Prove**, respectively . 3. In the CONSTRUCTION we apply the postulates , or problems that have been**proved**possible , to make such changes in the form or position of the given figures as may be needful for the demonstration . 4. In the ... Page 23

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**Prove**: No other line drawn through A can be to BD . For any other line drawn from A must lie between FC and AB or between FC and AD . Let it lie between FC and AD , as AE . Because CAB = CAD , ( Hyp . ) but EAB > < CAB , and EAD < CAD ... Page 25

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**Prove**: BAC and CAD are supplementary angles . Since AB is in a straight line with AD , BAD is a straight Z. ( Hyp . ) ( 29 ) ( 28 ) But BAC + / CAD = Z BAD , .. BAC and CAD are supplementary . Q.E.D. ( 33 ) 47. COR . 1. The sum of all ... Page 26

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**Prove**Their exterior sides , AB , AD , are in a straight line . Since the BAC , CAD , are supplementary , ( Hyp . ) △ BAC + ≤ CAD = a straight 2 , .. their sum , △ BAD , is a straight △ , ( 33 ) .. AB and AD , the sides of BAD , are ... Page 27

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**Prove**: AC is not perpendicular to BC . Turn the figure ABC about BC till A takes the position a ' in the original plane . Mark the point 4 ' , restore ABC to its first position , and join A'B , A'C . Then since AB and AC can be made to ...### Contents

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### Common terms and phrases

ABē ABCD ACē altitude angle formed apothem arc AC bisector bisects chord circumf circumference circumscribed coincide cone of revolution Const construct cylinder DEFINITION diagonals diagram for Prop diameter dihedral angles divided draw edges equiangular equiangular polygon equidistant equilateral triangle equivalent EXERCISE find a point frustum given circle given line given point given straight line greater homologous hypotenuse inscribed intercept interior angles intersecting isosceles triangle line drawn line joining locus meet mid point number of sides numerical measures parallel parallelogram parallelopiped pass perimeter perpendicular plane MN polyhedral angle polyhedron prism produced PROPOSITION Prove pyramid quadrilateral radii radius ratio rect rectangle regular polygon regular polyhedrons right angle right triangle SCHOLIUM secant segment similar slant height sphere spherical polygon spherical triangle square straight angle tangent THEOREM triangle ABC trihedral vertex vertical angle volume

### Popular passages

Page 308 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...

Page 298 - Sphere is a body bounded by a uniformly curved surface, all the points of which are equally distant from a point within called the center.

Page 283 - 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.

Page 113 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.

Page 373 - The object of these primers is to convey information in such a manner as to make it both intelligible and interesting to very young pupils, and so to discipline their minds as to incline them to more systematic after-studies. They are not only an aid to the pupil, but to the teacher, lightening the task of each by an agreeable, easy, and natural method of instruction.

Page 178 - ... the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle.

Page 123 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.

Page 118 - If the product of two numbers is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.

Page 179 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle.

Page 272 - Two prisms are to each other as the products of their bases by their altitudes ; prisms having equivalent bases are to each other as their altitudes; prisms having equal altitudes are to each other as their bases ; prisms having equivalent bases and equal altitudes are equivalent.