Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of EuclidJ. Johnson, 1789 - 272 sider |
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Side 123
... half the fide of the fquare AD or AB ) , whence the fide GE will also be equal to the fide EF . And , in the fame manner , it may be proved , that HE , EK are each equal to GE and EF . The lines EF , EG , EH and EK are , therefore , all ...
... half the fide of the fquare AD or AB ) , whence the fide GE will also be equal to the fide EF . And , in the fame manner , it may be proved , that HE , EK are each equal to GE and EF . The lines EF , EG , EH and EK are , therefore , all ...
Side 130
... half the angle CDE ( by Conft . ) and the angle CDE is equal to the angle CBA ( by Hyp . ) ; confequently the angle CBO is alfo equal to half the angle CBA . The angle CBA , therefore , is bifected by the line вO ; and , in the fame ...
... half the angle CDE ( by Conft . ) and the angle CDE is equal to the angle CBA ( by Hyp . ) ; confequently the angle CBO is alfo equal to half the angle CBA . The angle CBA , therefore , is bifected by the line вO ; and , in the fame ...
Side 131
... half the angle CDE , ( by Conft . ) , and the angle CDE is equal to the angle CBA ( by Hyp . ) ; whence the angle CBO is also equal to half the angle CBA . The angle CBA , therefore , is bifected by the line вO ; and , in the fame ...
... half the angle CDE , ( by Conft . ) , and the angle CDE is equal to the angle CBA ( by Hyp . ) ; whence the angle CBO is also equal to half the angle CBA . The angle CBA , therefore , is bifected by the line вO ; and , in the fame ...
Side 184
... half the parallelograms AB , AC ( I. 30. ) ; whence DFA is to AEG as the rectangle of DA , AF is to the rectangle of GA , aɛ . Q. E. D. SCHOLIUM . If the line EF be drawn , the latter part of this propofition may be proved from the ...
... half the parallelograms AB , AC ( I. 30. ) ; whence DFA is to AEG as the rectangle of DA , AF is to the rectangle of GA , aɛ . Q. E. D. SCHOLIUM . If the line EF be drawn , the latter part of this propofition may be proved from the ...
Side 188
... half the given line . Let AB be the given line , and c the fide of the given fquare ; it is required to divide AB into two fuch parts that their rectangle may be equal to the fquare of c . Upon AB describe the femicircle BDA , and make ...
... half the given line . Let AB be the given line , and c the fide of the given fquare ; it is required to divide AB into two fuch parts that their rectangle may be equal to the fquare of c . Upon AB describe the femicircle BDA , and make ...
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Elements of Geometry: Containing the Principal Propositions in the First Six ... Euclid,John Bonnycastle Ingen forhåndsvisning - 2016 |
Almindelige termer og sætninger
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
Populære passager
Side 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.
Side 73 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.