Elements of Geometry: With Practical Applications to Mensuration |
From inside the book
Results 1-5 of 100
Page 9
... perpendicular to each other , when their meeting forms equal adjacent angles ; thus the lines A B and CD are perpendicular to each other . B C A -D Two adjacent angles , as C A B and BAD , have a com- mon vertex , as A ; and a common ...
... perpendicular to each other , when their meeting forms equal adjacent angles ; thus the lines A B and CD are perpendicular to each other . B C A -D Two adjacent angles , as C A B and BAD , have a com- mon vertex , as A ; and a common ...
Page 23
... perpendicular can be drawn to DE . D A E CB F Let it be supposed that we can draw two perpendiculars , AB and A C. Produce one of them , as A B , till BF is equal to A B , and join F C. Then , in the triangles A B C and CBF , the angles ...
... perpendicular can be drawn to DE . D A E CB F Let it be supposed that we can draw two perpendiculars , AB and A C. Produce one of them , as A B , till BF is equal to A B , and join F C. Then , in the triangles A B C and CBF , the angles ...
Page 24
... perpendicular can be drawn from the same point to the same straight line . F E D 71. Cor . At the same point C , in the line A B , it is likewise impossible to erect more than one perpendicular to that line . For , if CD and CE were ...
... perpendicular can be drawn from the same point to the same straight line . F E D 71. Cor . At the same point C , in the line A B , it is likewise impossible to erect more than one perpendicular to that line . For , if CD and CE were ...
Page 25
... perpendicular to De , and the oblique lines A E , A C , A D. Produce AB till BF is equal to A B , and join CF , DF . First . The triangle BCF is equal to the triangle BCA , for D A E C B F they have the side C B common , the side A B ...
... perpendicular to De , and the oblique lines A E , A C , A D. Produce AB till BF is equal to A B , and join CF , DF . First . The triangle BCF is equal to the triangle BCA , for D A E C B F they have the side C B common , the side A B ...
Page 26
... perpendicular will be un- equally distant from those extremities . Let DC be drawn perpendicular to the straight line AB , from its middle point C. First . Let D and E be points , taken at pleasure , in the perpendicular , and join DA ...
... perpendicular will be un- equally distant from those extremities . Let DC be drawn perpendicular to the straight line AB , from its middle point C. First . Let D and E be points , taken at pleasure , in the perpendicular , and join DA ...
Other editions - View all
Common terms and phrases
A B C ABCD adjacent angles altitude angle ACB angle equal arc A B base bisect chord circle circumference circumscribed cone convex surface cosec Cosine Cotang cylinder diagonal diameter distance divided drawn equal Prop equilateral triangle equivalent exterior angle feet formed frustum gles greater half the sum hence homologous hypothenuse inches included angle inscribed isosceles less Let ABC line A B logarithmic sine measured by half multiplied number of sides parallel parallelogram parallelopipedon pendicular perimeter perpendicular polyedron prism PROBLEM PROPOSITION pyramid quadrantal radii radius ratio rectangle regular polygon right angles right-angled triangle rods Scholium secant segment side A B similar slant height solve the triangle sphere spherical polygon spherical triangle Tang tangent THEOREM triangle ABC triangle equal trigonometric functions vertex
Popular passages
Page 59 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 37 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 120 - At a point in a given straight line to make an angle equal to a given angle.
Page 52 - 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 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 199 - Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions.
Page 121 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 103 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 2 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art.
Page 2 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.