Plane and Solid Geometry |
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Page 6
... coincide . Thus , the angles AOB and A'O'B ' are equal , if A'O'B ' can be superposed upon AOB so that while O'A ' coincides with OA , O'B ' shall also coin- cide with OB , or when the difference in the directions of the sides of one ...
... coincide . Thus , the angles AOB and A'O'B ' are equal , if A'O'B ' can be superposed upon AOB so that while O'A ' coincides with OA , O'B ' shall also coin- cide with OB , or when the difference in the directions of the sides of one ...
Page 10
... coincides with CB . Hence CB is in the same straight line with CA. PROPOSITION III . THEOREM . 49. If two straight lines intersect each other , the vertical angles are equal . C A B E D Let the straight lines AB and CD intersect at E ...
... coincides with CB . Hence CB is in the same straight line with CA. PROPOSITION III . THEOREM . 49. If two straight lines intersect each other , the vertical angles are equal . C A B E D Let the straight lines AB and CD intersect at E ...
Page 12
... coincide with P ' , and , Q remaining stationary , PQ will fall upon P'Q . Therefore , if / PQO be a right angle , Z P'QO must also be a right angle , and ( from 48 ) the lines PQP ' must be straight ; this would give two straight lines ...
... coincide with P ' , and , Q remaining stationary , PQ will fall upon P'Q . Therefore , if / PQO be a right angle , Z P'QO must also be a right angle , and ( from 48 ) the lines PQP ' must be straight ; this would give two straight lines ...
Page 14
... coincide with CBD . and .. Z CAD / CBD , = ZACD = / DCB ; C E -F A D B that is , the two equal oblique lines drawn from the same point in the perpendicular make equal angles with the perpendicular and also with the base . 56. COR . 3 ...
... coincide with CBD . and .. Z CAD / CBD , = ZACD = / DCB ; C E -F A D B that is , the two equal oblique lines drawn from the same point in the perpendicular make equal angles with the perpendicular and also with the base . 56. COR . 3 ...
Page 27
... coincide with the line joining BC , or the triangles will coincide throughout , and hence are equal . Q.E.D. 87. SCHOLIUM . In equal figures , lines or angles similarly situated are called Homologous . PROPOSITION XIV . THEOREM . 88 ...
... coincide with the line joining BC , or the triangles will coincide throughout , and hence are equal . Q.E.D. 87. SCHOLIUM . In equal figures , lines or angles similarly situated are called Homologous . PROPOSITION XIV . THEOREM . 88 ...
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Common terms and phrases
ABCD AC² acute angle AD² adjacent adjacent angles altitude angle formed angles are equal apothem arc BC base and altitude bisect bisector called centre chord circumference circumscribed cone cylinder diagonals diameter diedral angles distance divided draw drawn ECDH equally distant equilateral equivalent EXERCISES faces four right angles frustum given point given straight line hence homologous homologous sides hypotenuse inscribed polygon interior angles intersection isosceles triangle join lateral area lateral edges Let ABC lune mean proportional measured by one-half middle point number of sides parallelogram parallelopiped perimeter perpendicular polyedral angle polyedron PROPOSITION XI prove pyramid Q.E.D. PROPOSITION quadrilateral radii radius ratio rectangle rectangular parallelopiped regular polygon right triangle SCHOLIUM segments semiperimeter sphere spherical angle spherical polygon spherical triangle surface tangent THEOREM triangle ABC triangles are equal triangular triangular prism V-ABC vertex vertical angle
Popular passages
Page 46 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Page 105 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.
Page 82 - 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 192 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 108 - 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 146 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Page 30 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 80 - In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Page 79 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = ос.
Page 148 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.