Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of EuclidJ. Johnson, 1789 - 272 páginas |
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Página 25
... distance ED , defcribe the circle KHD , cutting DG in K ; and from the point F , with the diftance FG , defcribe the circle GHL , cutting DG in L. Then , because EG is greater than ED ( by Hyp . ) , or its equal EK , the point G , which ...
... distance ED , defcribe the circle KHD , cutting DG in K ; and from the point F , with the diftance FG , defcribe the circle GHL , cutting DG in L. Then , because EG is greater than ED ( by Hyp . ) , or its equal EK , the point G , which ...
Página 35
... distances CD , ED , defcribe the arcs rs , nm . Then , fince any two fides of the triangle ECD are , to- gether , greater than the third fide ( Prop . 18. ) , thofe arcs will interfect each other ( Prop . 19. ) Let them interfect at F ...
... distances CD , ED , defcribe the arcs rs , nm . Then , fince any two fides of the triangle ECD are , to- gether , greater than the third fide ( Prop . 18. ) , thofe arcs will interfect each other ( Prop . 19. ) Let them interfect at F ...
Página 65
... distance of the perpendicu- lar from the obtuse angle . Д B Let ABC be a triangle , of which ABC is an obtufe an- gle , and CD perpendicular to AB ; then will the fquare of AC be greater than the fquares of AB , BC , by twice the ...
... distance of the perpendicu- lar from the obtuse angle . Д B Let ABC be a triangle , of which ABC is an obtufe an- gle , and CD perpendicular to AB ; then will the fquare of AC be greater than the fquares of AB , BC , by twice the ...
Página 66
... distance of the perpendicular from the acute angle . ΔΔ Let ABC be a triangle , of which ABC is an acute an- gle , and CD perpendicular to AB : then will the square of AC , be less than the fum of the fquares of AB and Bc , by twice the ...
... distance of the perpendicular from the acute angle . ΔΔ Let ABC be a triangle , of which ABC is an acute an- gle , and CD perpendicular to AB : then will the square of AC , be less than the fum of the fquares of AB and Bc , by twice the ...
Página 84
... distances from the centre , be equal to each other . For the fquares of AC , co are equal to the fquare of OA ( II . 14. ) , and the fquares of DF , FO to the fquare of OD . But the fquare of OA is equal to the fquare of OD ( II . 2 ...
... distances from the centre , be equal to each other . For the fquares of AC , co are equal to the fquare of OA ( II . 14. ) , and the fquares of DF , FO to the fquare of OD . But the fquare of OA is equal to the fquare of OD ( II . 2 ...
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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 AC is equal alfo equal alſo be equal alſo be greater altitude angle ABC angle ACB angle BAC angle CAB angle DAF bafe baſe becauſe bifect cafe centre chord circle ABC circumference Conft defcribe demonftration diagonal diameter diſtance draw EFGH equiangular equimultiples EUCLID fame manner fame multiple fame plane fame ratio fecond fection fegment fhewn fide AB fide AC fimilar fince the angles folid fome fquares of AC ftand given circle given right line infcribed interfect join the points lefs leſs Let ABC magnitudes muſt oppofite angles outward angle parallelepipedons parallelogram perpendicular polygon prifm propofition proportional Q. E. D. PROP reafon rectangle of AB rectangle of AC remaining angle right angles SCHOLIUM ſhall ſpace ſquare tangent THEOREM theſe thofe thoſe triangle ABC twice the rectangle whence
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.