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 interfection C , ABC will be the equilateral triangle re- quired .
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 interfection C , ABC will be the equilateral triangle re- quired .
Página 8
3. ) , cutting DA produced in G , and AG will be equal to BC , as was required . For , fince в 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 , fince в 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 alfo coincide with the fide FE . And , fince 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 alfo coincide with the fide FE . And , fince CA is equal to FD , and CB to FE ( by Hyp . ) , the point A will fall upon the ...
Página 11
3 ) , and join the points AE , BD : Then , because the two fides CA , CE of the triangle CAE , are equal to the two fides CB , CD of the triangle CBD , and the angle c is commòn , the fide AE will also be equal to the fide BD ...
3 ) , and join the points AE , BD : Then , because the two fides CA , CE of the triangle CAE , are equal to the two fides CB , CD of the triangle CBD , and the angle c is commòn , the fide AE will also be equal to the fide BD ...
Página 12
Then , because the two fides AD , AB , of the triangle ADB , are equal to the two fides 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 fides AD , AB , of the triangle ADB , are equal to the two fides 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 ...
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Elements of Geometry: Containing the Principal Propositions in the First Six ... Euclid,John Bonnycastle Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD alfo alfo equal alſo be equal altitude angle ABC angle ACB angle BAD bafe baſe becauſe bifect Book centre chord circle ABC circumference common confequently Conft contained defcribe definition demonftration diagonal diameter difference divided double draw drawn Elements equiangular equimultiples EUCLID fall fame manner fame multiple fame ratio fection fegment fhewn fide fide AC figure fince folid fome four fquare fquares of AC given given right line greater half interfect lefs leſs Let ABC magnitudes mean meet parallel parallelogram perpendicular plane polygon PROBLEM produced PROP propofition proportional proved Q. E. D. PROP reaſon rectangle right angles right line ſquare taken tangent THEOREM theſe thing third thofe triangle triangle ABC twice VIII whence whole
Pasajes populares
Página 166 - 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 73 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 215 - 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 117 - 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 18 - 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 249 - 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 102 - 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 i - Handbook to the First London BA Examination. Lie (Jonas). SECOND SIGHT; OR, SKETCHES FROM NORDLAND. By JONAS LIE. Translated from the Norwegian. [/» preparation. Euclid. THE ENUNCIATIONS AND COROLLARIES of the Propositions in the First Six and the Eleventh and Twelfth Books of Euclid's Elements.
Página 5 - 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 145 - 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.
Información bibliográfica
| Título | Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of Euclid |
| Autor | Euclid |
| Editor | John Bonnycastle |
| Editor | J. Johnson, no. 72, St. Paul's Church-Yard., 1789 |
| Procedencia del original | Biblioteca Pública de Nueva York |
| Digitalizado | 21 Jun. 2006 |
| Largo | 272 páginas |
| Exportar cita | BiBTeX EndNote RefMan |