An Elementary Geometry |
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Page 10
... THEOREM VII . 33. The sum of the angles of a triangle is equal to two right angles . Let ABC be a triangle ; the sum ... ( 7 ) ; A + B + BCA = two right angles . 34. Cor . 1. If two angles of a triangle are known , the third can be ...
... THEOREM VII . 33. The sum of the angles of a triangle is equal to two right angles . Let ABC be a triangle ; the sum ... ( 7 ) ; A + B + BCA = two right angles . 34. Cor . 1. If two angles of a triangle are known , the third can be ...
Page 22
... Theorem VII . by first drawing a line through B par- allel to A C. 75. Prove Theorem VII . by drawing a triangle upon the floor , walking over its perimeter , and turning at each vertex through an angle equal to the angle at that vertex ...
... Theorem VII . by first drawing a line through B par- allel to A C. 75. Prove Theorem VII . by drawing a triangle upon the floor , walking over its perimeter , and turning at each vertex through an angle equal to the angle at that vertex ...
Page 29
... THEOREM VII . 20. Equimultiples of two quantities have the same ratio as the quantities themselves . For that is a ma b mb a : b = ma : mb 21. Corollary . It follows that either couplet of a proportion may be multiplied or divided by ...
... THEOREM VII . 20. Equimultiples of two quantities have the same ratio as the quantities themselves . For that is a ma b mb a : b = ma : mb 21. Corollary . It follows that either couplet of a proportion may be multiplied or divided by ...
Page 35
... THEOREM VII . CONVERSE OF THEOREM VI . 18. A line dividing two sides of a triangle proportionally is parallel to the third side of the triangle . In the triangle ABC if DE divides AB and AC so that AE : EC = AD : DB , then DE is ...
... THEOREM VII . CONVERSE OF THEOREM VI . 18. A line dividing two sides of a triangle proportionally is parallel to the third side of the triangle . In the triangle ABC if DE divides AB and AC so that AE : EC = AD : DB , then DE is ...
Page 54
... THEOREM VI . A B A D B C D E 24. Every equilateral polygon inscribed in a circle is regular . Let ABCDEF be an ... THEOREM VII . 25. An infinitely small chord coincides with its arc . Let AB be an infinitely small chord ; it ...
... THEOREM VI . A B A D B C D E 24. Every equilateral polygon inscribed in a circle is regular . Let ABCDEF be an ... THEOREM VII . 25. An infinitely small chord coincides with its arc . Let AB be an infinitely small chord ; it ...
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Common terms and phrases
ABC and DEF ABCD adjacent altitude angle ABC apothem base and altitude bisect centre chord circ circumference coincide cone construct the triangle convex surface Corollary cube cylinder diameter distance divided dodecagon EATON'S equal altitudes equally distant equiangular equilateral feet frustum given angle given circle given line given point given side given square given triangle half the arc hexagon homologous sides hypothenuse included angle infinite number inscribed internal angles intersection isosceles triangle Let ABCDEF line joining mean proportional measured by half number of sides opposite sides parallel planes parallelogram parallelopiped perimeter perpendicular plane parallel propositions quadrilateral radii radius ratio rectangle regular polygon respectively equal rhombus right angles right prism right pyramid right triangle Scholium secant segment similar triangles slant height sphere tangent THEOREM VIII trapezoid triangle ABC vertex
Popular passages
Page 25 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Page 30 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 27 - If the product of two quantities is equal to the product of two others, the...
Page 43 - The area of a regular polygon is equal to half the product of its perimeter and apothem.
Page 11 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 23 - If two triangles have two sides of one respectively equal to two sides of the other, but the third sides unequal...
Page 20 - ... polygon, is equal to twice as many right angles as the polygon has sides minus two.
Page 49 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 70 - A right cylinder is a solid described by the revolution of a rectangle about one of its sides.
Page 64 - DEFINITIONS. 1 . A straight line is perpendicular to a plane, when it is perpendicular to every straight line of the plane which it meets.