Chauvenet's Treatise on Elementary Geometry |
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Page 52
... circumference . Any straight line drawn from the centre to the circumference is called a radius . Any straight line drawn through the centre . and terminated each way by the circumfer- ence is called a diameter . C D E F B A In the ...
... circumference . Any straight line drawn from the centre to the circumference is called a radius . Any straight line drawn through the centre . and terminated each way by the circumfer- ence is called a diameter . C D E F B A In the ...
Page 53
... circumference may be described with any point as a centre and any distance as a radius . ARCS AND CHORDS . PROPOSITION I. - THEOREM . 6. A straight line cannot intersect a circumference in more than two points . For , if it could ...
... circumference may be described with any point as a centre and any distance as a radius . ARCS AND CHORDS . PROPOSITION I. - THEOREM . 6. A straight line cannot intersect a circumference in more than two points . For , if it could ...
Page 54
... circumference . Let AMBN be a circle whose centre is 0 ; then , any diameter AOB bisects the circle and its circumference . M N B For , if the figure ANB be turned about AB as an axis and superposed upon the figure AMB , the curve ANB ...
... circumference . Let AMBN be a circle whose centre is 0 ; then , any diameter AOB bisects the circle and its circumference . M N B For , if the figure ANB be turned about AB as an axis and superposed upon the figure AMB , the curve ANB ...
Page 58
... circumference described from O as a centre and a radius equal to any one of the three equal distances OA , OB , OC , will pass through the three given points . 2d . Only one circumference can be made to pass through these points . For ...
... circumference described from O as a centre and a radius equal to any one of the three equal distances OA , OB , OC , will pass through the three given points . 2d . Only one circumference can be made to pass through these points . For ...
Page 59
... circumference . In the same case , the circle is said to be in- scribed in the figure . B о PROPOSITION X. - THEOREM ... circumference . Therefore AB cuts the circumference in C , and must evi- dently cut it in a second point D ...
... circumference . In the same case , the circle is said to be in- scribed in the figure . B о PROPOSITION X. - THEOREM ... circumference . Therefore AB cuts the circumference in C , and must evi- dently cut it in a second point D ...
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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.