Elementary GeometryJ.B. Lippincott Company, 1893 |
From inside the book
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Page 29
... one respectively equal to the hypotenuse and an adjacent angle of the other . Suggestion . Superpose the second ... half of PP ' , is less than PD , the half of PDP ' . EXERCISES . 1. Theorem . - Two oblique lines drawn from a point to a ...
... one respectively equal to the hypotenuse and an adjacent angle of the other . Suggestion . Superpose the second ... half of PP ' , is less than PD , the half of PDP ' . EXERCISES . 1. Theorem . - Two oblique lines drawn from a point to a ...
Page 49
... one - half the vertical angle . 8. If the vertical angle of an isosceles triangle is one - half as great as an angle at the base , a line bisecting a base angle will divide the given triangle into two isosceles triangles . 9. If two ...
... one - half the vertical angle . 8. If the vertical angle of an isosceles triangle is one - half as great as an angle at the base , a line bisecting a base angle will divide the given triangle into two isosceles triangles . 9. If two ...
Page 50
... one - half the angle A. E A B C 13. The medial line to any side of a triangle is less than the half sum of the other two sides . Definition . A line joining a vertex of a triangle B with the middle point of the opposite side is called a ...
... one - half the angle A. E A B C 13. The medial line to any side of a triangle is less than the half sum of the other two sides . Definition . A line joining a vertex of a triangle B with the middle point of the opposite side is called a ...
Page 52
... one - half their sum . B E Suggestion . Draw HG parallel to AB , and extend AD . DGF = CHF ( Proposition VII ... one of the sides , it also bisects the other side ; and the portion of it intercepted between the two sides is equal to one ...
... one - half their sum . B E Suggestion . Draw HG parallel to AB , and extend AD . DGF = CHF ( Proposition VII ... one of the sides , it also bisects the other side ; and the portion of it intercepted between the two sides is equal to one ...
Page 57
... one - half the circle , as the segment AMB , is called a semicircle . An arc equal to half a circumference , as the arc AMB , is called a semi - circum- ference . PROPOSITION III . - THEOREM . 8. In equal circles BOOK II . 57.
... one - half the circle , as the segment AMB , is called a semicircle . An arc equal to half a circumference , as the arc AMB , is called a semi - circum- ference . PROPOSITION III . - THEOREM . 8. In equal circles BOOK II . 57.
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Common terms and phrases
ABCD adjacent angles altitude angle BAC angles are equal apothem bisects centre chord coincide common cone construct convex Corollary cylinder Definition diagonal diameter dicular diedral angle distance divided draw equal circles equally distant equilateral equivalent Exercise find the locus frustum given circle given line given point given straight line greater Hence hypotenuse included angle inscribed angle intercepted arcs isosceles triangle lateral area lateral edges mean proportional middle point number of sides parallel lines parallelogram parallelopiped pass a plane pendicular perimeter perpen perpendicular plane MN plane passed polyedral angle Proposition VI Proposition VII quadrilateral radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right triangle Scholium secant secant line segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron Theorem triangle ABC triangles are equal triangular prism triedral upper base vertex volume
Popular passages
Page 127 - The area of a rectangle is equal to the product of its base and altitude.
Page 196 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Page 131 - Two triangles having 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 245 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Page 278 - A lune is to the, surface of the sphere as the angle of the lune is to four right angles. Let...
Page 111 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 48 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Page 57 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 34 - The sum of the three angles of any triangle is equal to two right angles.