Elements of Geometry and Trigonometry |
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Page 12
... means of a train of reasoning called a demonstration . A problem is a question proposed , which requires a solu- tion . A lemma is a subsidiary truth , employed for the demonstra- tion of a theorem , or the solution of a problem . The ...
... means of a train of reasoning called a demonstration . A problem is a question proposed , which requires a solu- tion . A lemma is a subsidiary truth , employed for the demonstra- tion of a theorem , or the solution of a problem . The ...
Page 13
... means the square - root of 2 ; √A × B means the square - root of the product of A and B. Axioms . 1 1. Things which are equal to the same thing , are equal to each other . 2. If equals be added to equals , the wholes will be equal . 3 ...
... means the square - root of 2 ; √A × B means the square - root of the product of A and B. Axioms . 1 1. Things which are equal to the same thing , are equal to each other . 2. If equals be added to equals , the wholes will be equal . 3 ...
Page 35
... means . 3. Of four proportional quantities , the first and third are called the antecedents , and the second and ... mean proportional between the other two . 5. Magnitudes are said to be in proportion by inversion , or inversely , when ...
... means . 3. Of four proportional quantities , the first and third are called the antecedents , and the second and ... mean proportional between the other two . 5. Magnitudes are said to be in proportion by inversion , or inversely , when ...
Page 36
... mean . PROPOSITION II . THEOREM . If the product of two quantities be equal to the product of two other quantities , two of them will be the extremes and the other two the means of a proportion . 4 Let MxQ = Nx P ; then will M : N :: P ...
... mean . PROPOSITION II . THEOREM . If the product of two quantities be equal to the product of two other quantities , two of them will be the extremes and the other two the means of a proportion . 4 Let MxQ = Nx P ; then will M : N :: P ...
Page 37
... means of the four quantities N , M , Q , P , and these products being equal , Ñ : M :: Q : P ( Prop . II . ) . PROPOSITION VI . THEOREM . If four quantities are in proportion , they will be in proportion by composition , or division ...
... means of the four quantities N , M , Q , P , and these products being equal , Ñ : M :: Q : P ( Prop . II . ) . PROPOSITION VI . THEOREM . If four quantities are in proportion , they will be in proportion by composition , or division ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex