Elements of Geometry and Trigonometry |
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Page 11
... equal ; ́an isosceles triangle , one which has two of its sides equal ; a scalene triangle , one which has its three sides unequal . 16. A right - angled triangle is one which has a right angle . The side opposite the right angle is ...
... equal ; ́an isosceles triangle , one which has two of its sides equal ; a scalene triangle , one which has its three sides unequal . 16. A right - angled triangle is one which has a right angle . The side opposite the right angle is ...
Page 13
... equal to the same thing , are equal to each other . 2. If equals be added to equals , the wholes will be equal . 3. If equals be taken from equals , the remainders will be equal . 4. If equals be added to unequals , the wholes will be un- ...
... equal to the same thing , are equal to each other . 2. If equals be added to equals , the wholes will be equal . 3. If equals be taken from equals , the remainders will be equal . 4. If equals be added to unequals , the wholes will be un- ...
Page 14
... equal to two right angles . A E B Let the straight line DC meet the straight line AB at C , then will the angle ACD + the angle DCB , be equal to two right angles . At the point C , erect CE perpendicular to AB . The angle ACD is the ...
... equal to two right angles . A E B Let the straight line DC meet the straight line AB at C , then will the angle ACD + the angle DCB , be equal to two right angles . At the point C , erect CE perpendicular to AB . The angle ACD is the ...
Page 15
... equal to the angel FCE ( Ax . 10. ) ; which can only be the case when the lines CD and CE coincide : there- fore , the straight lines which have two points A and B com- mon , cannot separate at any point , when produced ; hence they ...
... equal to the angel FCE ( Ax . 10. ) ; which can only be the case when the lines CD and CE coincide : there- fore , the straight lines which have two points A and B com- mon , cannot separate at any point , when produced ; hence they ...
Page 16
... equal to two right angles : hence the sum ACE + ACD is equal to the sum ACE + ECB ( Ax . 1. ) . Take away from both , the com- mon angle ACE , there remains the angle ACD , equal to its opposite or vertical angle ECB ( Ax . 3 ...
... equal to two right angles : hence the sum ACE + ACD is equal to the sum ACE + ECB ( Ax . 1. ) . Take away from both , the com- mon angle ACE , there remains the angle ACD , equal to its opposite or vertical angle ECB ( Ax . 3 ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine cotangent cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex