Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of Euclid |
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Página 7
Then , because the two circles pass through each other's centres , they will cut each other . And , if the right lines CA , CB be drawn from the point of intersection c , Abe will be the equilateral triangle required .
Then , because the two circles pass through each other's centres , they will cut each other . And , if the right lines CA , CB be drawn from the point of intersection c , Abe will be the equilateral triangle required .
Página 8
3. ) , cutting DA produced in G , and AG will be equal to BC , as was required . For , since B is the centre of the circle CEF , Bc is equal to bf ( Def . 13. ) And , because D is the centre of the circle FHG , DG is equal to DF ( Def .
3. ) , cutting DA produced in G , and AG will be equal to BC , as was required . For , since B is the centre of the circle CEF , Bc is equal to bf ( Def . 13. ) And , because D is the centre of the circle FHG , DG is equal to DF ( Def .
Página 10
Then , because CA coincides with FD , and the angle c is equal to the angle F ( by Hyp . ) , the fide CB will also coincide with the side Fe . And , since ca is equal to FD , and CB to Fe ( by Hyp . ) , the point A will fall upon the ...
Then , because CA coincides with FD , and the angle c is equal to the angle F ( by Hyp . ) , the fide CB will also coincide with the side Fe . And , since ca is equal to FD , and CB to Fe ( by Hyp . ) , the point A will fall upon the ...
Página 12
Then , because the two sides AD , AB , of the triangle ADB , are equal to the two sides BC , BA , of the triangle ACB , and the angle DAB is equal to the angle CBA ( by Hyp . ) , the triangle ADB will be equal to the triangle ACB ( Prop ...
Then , because the two sides AD , AB , of the triangle ADB , are equal to the two sides BC , BA , of the triangle ACB , and the angle DAB is equal to the angle CBA ( by Hyp . ) , the triangle ADB will be equal to the triangle ACB ( Prop ...
Página 13
And , because the side bc is equal to the side EF , or BG ( by Hyp . ) , the angle BCG will be equal to the angle BGC ( Prop . 5. ) But since the angles ACG , BCG are equal to the angles AGC , BGC , each to each ...
And , because the side bc is equal to the side EF , or BG ( by Hyp . ) , the angle BCG will be equal to the angle BGC ( Prop . 5. ) But since the angles ACG , BCG are equal to the angles AGC , BGC , each to each ...
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Otras ediciones - Ver todas
Elements of Geometry: Containing the Principal Propositions in the First Six ... John Bonnycastle Sin vista previa disponible - 2017 |
Términos y frases comunes
ABCD alſo be equal alſo equal altitude angle ABC angle ACB baſe becauſe biſect Book caſe centre chord circle circle ABC circumference common Conft conſequently contained definition demonſtrated deſcribe diagonal diameter difference diſtances divided double draw drawn equiangular equimultiples EUCLID fall fame fide figure fince firſt four given given right line greater half inſcribed interſects leſs Let ABC magnitudes mean meet muſt parallel parallelogram perpendicular plane polygon priſm PROBLEM produced Prop proportional propoſition proved reaſon rectangle right angles right line ſame ſame manner ſame multiple ſame ratio ſection ſegment ſhall ſhewn ſide ſince ſolid ſome ſquares of AC ſtand ſum taken tangent THEOREM theſe thing third thoſe triangle triangle ABC twice VIII whence whole
Pasajes populares
Página 164 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 71 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 213 - Lemma, if from the greater of two unequal magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there shall at length remain a magnitude less than the least of the proposed magnitudes.
Página 115 - In a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF. Draw the straight line GAH touching the circle in the point A (III. 17), and at the point A, in the straight line AH, make the angle HAG equal to the angle DEF (I.
Página 16 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. LET ab be the given straight line, which may be produced to any length both ways, and let c be a point without it. It is required to draw a straight line perpendicular to ab from the point c.
Página 247 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Página 100 - To bisect a given arc, that is, to divide it into two equal parts. Let ADB be the given arc : it is required to bisect it.
Página 3 - AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal.
Página 143 - F is greater than E; and if equal, equal; and if less, less. But F is any multiple whatever of C, and D and E are any equimultiples whatever of A and B; [Construction.