The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry, from the Edition of Dr. Robert Simson ... With ExercisesCharles Henry Law, 1854 - 120 páginas |
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Página 76
Euclid, Samuel A. GOOD. PROP . XIII . -THEOREM . One circle cannot touch another in more points than one , whether it touches it on the inside or outside . For , if it be possible , let the circle EBF touch the circle ABC in more points ...
Euclid, Samuel A. GOOD. PROP . XIII . -THEOREM . One circle cannot touch another in more points than one , whether it touches it on the inside or outside . For , if it be possible , let the circle EBF touch the circle ABC in more points ...
Página 80
... circle , as AC ; and draw DC to the point C where it meets the circumference . And because DA is equal ( I. Def . 15 ... touches the circle ( III . Def . 2. ) ; and 80 EUCLID'S ELEMENTS .
... circle , as AC ; and draw DC to the point C where it meets the circumference . And because DA is equal ( I. Def . 15 ... touches the circle ( III . Def . 2. ) ; and 80 EUCLID'S ELEMENTS .
Página 81
... touches it only in one point , because , if it did meet the circle in two , it would fall within it ( III . 2. ) . " Also it is evident that there can be but one straight line which touches the circle in the same point . " PROP . XVII ...
... touches it only in one point , because , if it did meet the circle in two , it would fall within it ( III . 2. ) . " Also it is evident that there can be but one straight line which touches the circle in the same point . " PROP . XVII ...
Página 82
... touches a circle , the straight line drawn from the centre to the point of contact , shall be perpendicular to the line touching the circle . Let the straight line DE touch the circle ABC in the point C ; take ( III . 1. ) the centre F ...
... touches a circle , the straight line drawn from the centre to the point of contact , shall be perpendicular to the line touching the circle . Let the straight line DE touch the circle ABC in the point C ; take ( III . 1. ) the centre F ...
Página 93
... touches the circle ABCD in the point B , and BA is drawn at right angles to the touching line from the point of contact B , ( III . 19. ) 1. The centre of the circle ABCD is in BA ; therefore ( III . 31. ) 2. The angle ADB in a ...
... touches the circle ABCD in the point B , and BA is drawn at right angles to the touching line from the point of contact B , ( III . 19. ) 1. The centre of the circle ABCD is in BA ; therefore ( III . 31. ) 2. The angle ADB in a ...
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Términos y frases comunes
AB is equal AC is equal adjacent angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal base BC bisected circle ABC circumference diameter double draw equal angles equal Constr equal Hyp equal straight lines equal to BC equilateral and equiangular EUCLID'S ELEMENTS exterior angle given circle given point given rectilineal angle given straight line given triangle gnomon greater inscribed interior and opposite less Let ABC Let the straight likewise opposite angles parallel to CD parallelogram pentagon perpendicular point F produced Q.E.D. PROP rectangle AE rectangle contained remaining angle required to describe right angles semicircle side BC square of AC straight line AB straight line AC straight line drawn touches the circle triangle ABC twice the rectangle