The Elements of GeometryJ. Wiley & Sons, 1885 - 366 páginas |
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Página xii
... proportional Equality of ratios defined Third proportional , mean pro- portional Ratios compared • • • • 177 • 177 • 177 178 , 179 180-182 Ways of changing a propor- tion . I. Fundamental Geometric Proportions . ARTICLE 497-500 ...
... proportional Equality of ratios defined Third proportional , mean pro- portional Ratios compared • • • • 177 • 177 • 177 178 , 179 180-182 Ways of changing a propor- tion . I. Fundamental Geometric Proportions . ARTICLE 497-500 ...
Página xv
... proportional PAGE 333 332 844. To transform any polyhedral angle , 334 332 845 , 846. Area of a lune • fined 838. Symmetrical space angles • • 334 839. Steregon 840. Steradian • 332 847. Plane angle as measure of dihedral , 335 333 848 ...
... proportional PAGE 333 332 844. To transform any polyhedral angle , 334 332 845 , 846. Area of a lune • fined 838. Symmetrical space angles • • 334 839. Steregon 840. Steradian • 332 847. Plane angle as measure of dihedral , 335 333 848 ...
Página 177
... Proportional , or to form a Proportion . This is written A : B :: C : D , and read " A to B is the same as C to D. " The second pair of magnitudes may be of a different kind from the first pair . A and D are called the Extremes , B and ...
... Proportional , or to form a Proportion . This is written A : B :: C : D , and read " A to B is the same as C to D. " The second pair of magnitudes may be of a different kind from the first pair . A and D are called the Extremes , B and ...
Página 188
... proportional . D ' B A The figure ABCD is similar to A'B'C'D ' if ¥ A = 4 A ' , 4 B = ¥ B ' , etc. , and also AB : A'B ' :: BC : B'C ' :: CD : C'D ' :: etc. THEOREM V. 508. Mutually equiangular triangles are similar . G B H F C A ...
... proportional . D ' B A The figure ABCD is similar to A'B'C'D ' if ¥ A = 4 A ' , 4 B = ¥ B ' , etc. , and also AB : A'B ' :: BC : B'C ' :: CD : C'D ' :: etc. THEOREM V. 508. Mutually equiangular triangles are similar . G B H F C A ...
Página 190
... proportional , are similar . H B А I A TH HYPOTHESIS . B = & G , and AB : BC : :: FG : GH . △ ABC ~ △ FGH ( using ~ for the word " similar ” ) . GF , and draw F'L || AC , CONCLUSION . PROOF . In BA take BF ' .. △ F'BL ~ △ ABC ...
... proportional , are similar . H B А I A TH HYPOTHESIS . B = & G , and AB : BC : :: FG : GH . △ ABC ~ △ FGH ( using ~ for the word " similar ” ) . GF , and draw F'L || AC , CONCLUSION . PROOF . In BA take BF ' .. △ F'BL ~ △ ABC ...
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Términos y frases comunes
ABCD alternate angles angles are equal angles equal angles opposite base bisect called chord circumcenter coincide common commutative law CONCLUSION construction COROLLARY diagonal diameter divided draw end point equal are congruent equal sects equiangular equilateral equivalent exterior angle figure given line given point given sect greater greatest common divisor hypothenuse HYPOTHESIS included angle inscribed inscribed angle intercepted interior isosceles triangle less line perpendicular magnitudes meet multiples number of sides pair parallelogram pass perigon perimeter perpendicular bisector plane MN PROOF proportional quadrilateral radii radius ratio rectangle rectangle contained regular polygon respectively equal right angle Rule of Inversion sect joining segment sphere spherical polygon spherical triangle square straight angle subtended surface symmetrical tangent tetrahedron THEOREM THEOREM VII transversal triangles are congruent vertex vertices
Pasajes populares
Página 44 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Página 112 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Página 24 - A right-angled triangle is one which has a right angle. The side opposite the right angle is called the hypothenuse.
Página 190 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 270 - BC with the same radius. Then a line through A touching this arc will be the required parallel. Or, use a straight edge and triangle.
Página 101 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Página 266 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.
Página 13 - An Acute Angle is one which is less than a right angle.
Página 104 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Página 107 - In an obtuse-angled triangle the square on the side opposite the obtuse angle is greater than the sum of the squares on the other two sides by twice the rectangle contained by either side and the projection on it of the other side.