Elements of Geometry |
From inside the book
Page 9
... angle BA C , B namely , AB and AC , be prolonged , their extent of opening will not be altered , and the A size of ... each other so that the two adjacent angles formed by producing one of the lines through the vertex are equal . Thus if the ...
... angle BA C , B namely , AB and AC , be prolonged , their extent of opening will not be altered , and the A size of ... each other so that the two adjacent angles formed by producing one of the lines through the vertex are equal . Thus if the ...
Page 10
... between two right angles and the given angle . Thus A CD is the supplement of the angle D C B ; also D C B is the ... equal to four right angles , and the angular magnitude about a point on one side of a straight line drawn through that ...
... between two right angles and the given angle . Thus A CD is the supplement of the angle D C B ; also D C B is the ... equal to four right angles , and the angular magnitude about a point on one side of a straight line drawn through that ...
Page 11
... equal to four right angles ; and the sum of all the angles about a point on one ... each other , and may Ā be called supplementary adjacent angles . ON THE ... angle may be taken up , turned over , and put down , without altering the difference ...
... equal to four right angles ; and the sum of all the angles about a point on one ... each other , and may Ā be called supplementary adjacent angles . ON THE ... angle may be taken up , turned over , and put down , without altering the difference ...
Page 12
... angle A'B ' C " ; if the side BA fall between B'C ' and B'A ' in the direction B ' D , the angle ABC is less than A ... one continuous straight line AD equal to the sum of the lines A B and C D. : Again if we have the angles ABC and DEF ...
... angle A'B ' C " ; if the side BA fall between B'C ' and B'A ' in the direction B ' D , the angle ABC is less than A ... one continuous straight line AD equal to the sum of the lines A B and C D. : Again if we have the angles ABC and DEF ...
Page 23
... equal dis- tances from the foot of the 1 , are equal ) . CBCD + DB , ( a ... angle be a right angle , what is its complement ? 2. If an angle be a right ... one and the same straight line . 6. Show that the two straight lines which bisect ...
... equal dis- tances from the foot of the 1 , are equal ) . CBCD + DB , ( a ... angle be a right angle , what is its complement ? 2. If an angle be a right ... one and the same straight line . 6. Show that the two straight lines which bisect ...
Other editions - View all
Common terms and phrases
A B C D AABC AACB AB² ABCD adjacent angles apothem arc A B base and altitude BC² centre centre of symmetry circumference circumscribed construct a square COROLLARY decagon diagonals diameter divided Draw equal arcs equal distances equal respectively equiangular equiangular polygon equilateral equilateral polygon exterior angles figure given circle given line given polygon given square homologous sides hypotenuse intersecting isosceles Let A B Let ABC line A B measured by arc middle point number of sides parallelogram perpendicular plane polygon ABC polygon similar PROBLEM prove Q. E. D. PROPOSITION quadrilateral radii radius equal ratio rect rectangles regular inscribed regular polygon required to construct right angles right triangle SCHOLIUM segment semicircle similar polygons subtend symmetrical with respect tangent THEOREM triangle ABC vertex vertices
Popular passages
Page 40 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 126 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Page 136 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Page 207 - Construct a rectangle having the difference of its base and altitude equal to a given line, and its area equivalent to the sum of a given triangle and a given pentagon.
Page 202 - In any proportion, the product of the means is equal to the product of the extremes.
Page 142 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Page 175 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 72 - Every point in the bisector of an angle is equally distant from the sides of the angle ; and every point not in the bisector, but within the angle, is unequally distant from the sides of the angle.
Page 73 - A CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 146 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.