Chauvenet's Treatise on Elementary Geometry |
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Page 21
... equally distant from the extremities of the line ; 2d . Every point withou the perpendicular is unequally distant from the extremities of the line . Let AB be a finite straight line , and Cits BOOK I. 21.
... equally distant from the extremities of the line ; 2d . Every point withou the perpendicular is unequally distant from the extremities of the line . Let AB be a finite straight line , and Cits BOOK I. 21.
Page 22
... equally distant from A and B. For , since CA = CB , we have ( 30 ) PA : = PB . 2d . Any point Q without the perpendicular is unequally distant from A and B. For , Q being on one side or the other of the perpendicular , one of the lines ...
... equally distant from A and B. For , since CA = CB , we have ( 30 ) PA : = PB . 2d . Any point Q without the perpendicular is unequally distant from A and B. For , Q being on one side or the other of the perpendicular , one of the lines ...
Page 26
... equally distant . Let AB and CD be two indefinitely extended parallels ; G and H any two points in CD ; GE and HF the per- pendiculars from G and H upon AB . Then , GE and HF are also perpendicular to CD ( 46 ) , and measure the distance ...
... equally distant . Let AB and CD be two indefinitely extended parallels ; G and H any two points in CD ; GE and HF the per- pendiculars from G and H upon AB . Then , GE and HF are also perpendicular to CD ( 46 ) , and measure the distance ...
Page 32
... equally distant from D and G , the line EF is per- pendicular to DG at its middle point H ( 41 ) . Hence , if the figure DEF be revolved upon the line EF , H being a fixed point , HD will fall upon its equal HG , and the triangle DEF ...
... equally distant from D and G , the line EF is per- pendicular to DG at its middle point H ( 41 ) . Hence , if the figure DEF be revolved upon the line EF , H being a fixed point , HD will fall upon its equal HG , and the triangle DEF ...
Page 35
... equally distant . Let AB and CD be two indefinitely extended parallels ; G and H any two points in CD ; GE and HF the per- pendiculars from G and H upon AB . Then , GE and HF are also perpendicular to CD ( 46 ) , and measure the distance ...
... equally distant . Let AB and CD be two indefinitely extended parallels ; G and H any two points in CD ; GE and HF the per- pendiculars from G and H upon AB . Then , GE and HF are also perpendicular to CD ( 46 ) , and measure the distance ...
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Common terms and phrases
ABCD adjacent angles allel angle AOB angle BAC angles are equal apothem arc AC BC² bisector bisects called centre chord circum circumference coincide Corollary Definition diagonals diameter dicular distance divided draw equal angles equally distant exterior angle ference figure four right angles geometry given angle given point given straight line greater hence homologous sides hypotenuse inscribed inscribed angle intercepted arcs less Let ABC measured by one-half middle point number of sides oblique lines one-half the arc opposite sides parallel to BC parallelogram pendicular perimeter perpen perpendicular points of intersection produced proportion PROPOSITION quadrilateral quantities radii radius ratio rectangle regular polygon rhombus right angles right triangles Scholium secant line segment semi-circumference side AC sides are equal square straight line drawn symmetrical with respect tangent theorem triangle ABC triangles are equal vertex
Popular passages
Page 201 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 31 - The perpendicular is the shortest line that can be drawn from a point to a straight line. Let PC be the perpendicular, and PD any oblique line, from the point P to the line AB. Then PC < PD. For, produce PC to P', making CP
Page 201 - Words, Facts, and Phrases : A Dictionary of Curious, Quaint, and Out-of-the-Way Matters. By ELIEZER EDWARDS.
Page 120 - Any side of a spherical triangle is less than the sum of the other two.
Page 81 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Page 92 - Every point in the bisector of an angle is equally distant from the sides of the angle...
Page 58 - An angle formed by a tangent and a chord is measured by one-half the intercepted arc.