Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 57
... centre than the circumference . PROP . III . THEOR . If a straight line drawn through the centre of a circle bisect a straight line in the circle , which does not pass through the centre , it will cut that line at right angles ; and if ...
... centre than the circumference . PROP . III . THEOR . If a straight line drawn through the centre of a circle bisect a straight line in the circle , which does not pass through the centre , it will cut that line at right angles ; and if ...
Página 58
... centre ; for this perpendicular is the same as the one let fall from the centre on the same chord , since both of them passes through the middle of the chord . COR . 2. It likewise follows , that the perpendicular drawn through the ...
... centre ; for this perpendicular is the same as the one let fall from the centre on the same chord , since both of them passes through the middle of the chord . COR . 2. It likewise follows , that the perpendicular drawn through the ...
Página 59
... centre : join EC , and draw any straight line EFG meeting the circles in F and G and because E is the centre of the circle ABC , CE is equal to EF : Again , because E is the centre of the circle CDG , CE is equal to EG : but CE was ...
... centre : join EC , and draw any straight line EFG meeting the circles in F and G and because E is the centre of the circle ABC , CE is equal to EF : Again , because E is the centre of the circle CDG , CE is equal to EG : but CE was ...
Página 60
... centre , is equal to one more remote , which is impossible . COR . 1. Therefore , from any point not the centre , more than two equal lines cannot be drawn to the circumference . COR . 2. Consequently , that point from which three equal ...
... centre , is equal to one more remote , which is impossible . COR . 1. Therefore , from any point not the centre , more than two equal lines cannot be drawn to the circumference . COR . 2. Consequently , that point from which three equal ...
Página 61
... centre of the circle ABC , and join ME , MF , MC , MK , ML , MH : And because AM is equal to ME , if MD be added to each , AD is equal to EM and MD ; but EM and MD are greater ( 13. 1. ) than ED ; therefore also AD is greater than ED ...
... centre of the circle ABC , and join ME , MF , MC , MK , ML , MH : And because AM is equal to ME , if MD be added to each , AD is equal to EM and MD ; but EM and MD are greater ( 13. 1. ) than ED ; therefore also AD is greater than ED ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore