Euclid's Elements of Geometry, Bøker 1-6Henry Martyn Taylor The University Press, 1893 - 504 sider |
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Resultat 1-5 av 11
Side 331
... multiples of the first and the third be taken and the 3rd multiples of the second and the fourth , the multiples in order are 10 , 9 , 25 , 24 : here 10 is greater than 9 and 25 greater than 24 : but equality between the ratios is not ...
... multiples of the first and the third be taken and the 3rd multiples of the second and the fourth , the multiples in order are 10 , 9 , 25 , 24 : here 10 is greater than 9 and 25 greater than 24 : but equality between the ratios is not ...
Side 332
... multiples of the second and the fourth , the multiples in order are 22 , 21 , 55 , 56 : here 22 is greater than 21 and 55 not greater than 56 : and the fact is established that the ratio of 2 to 3 is greater than that of 5 to 8 ...
... multiples of the second and the fourth , the multiples in order are 22 , 21 , 55 , 56 : here 22 is greater than 21 and 55 not greater than 56 : and the fact is established that the ratio of 2 to 3 is greater than that of 5 to 8 ...
Side 336
... multiples , of A , B and some multiple , say the nth multiple , of C , such that m times A is greater than n times C , and m times B not greater than n times C ; ( Def . 7. ) therefore there is some number m such that m times A is ...
... multiples , of A , B and some multiple , say the nth multiple , of C , such that m times A is greater than n times C , and m times B not greater than n times C ; ( Def . 7. ) therefore there is some number m such that m times A is ...
Side 339
... multiples , of C and E , and some equimultiples , say the nth multiples , of D and F , such that m times C is greater than n times D and m times E not greater than n times F. ( Def . 7. ) Again , because A is to B as C to D , m times A ...
... multiples , of C and E , and some equimultiples , say the nth multiples , of D and F , such that m times C is greater than n times D and m times E not greater than n times F. ( Def . 7. ) Again , because A is to B as C to D , m times A ...
Side 341
... multiples , of A , B , and any equimultiples , say the nth multiples , of C , D. PROOF . Because m times A is to m times B as A to B , and because n times C is to n times D as C to D , ( Prop . 6. Coroll . ) and A is to B as C to D ...
... multiples , of A , B , and any equimultiples , say the nth multiples , of C , D. PROOF . Because m times A is to m times B as A to B , and because n times C is to n times D as C to D , ( Prop . 6. Coroll . ) and A is to B as C to D ...
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Vanlige uttrykk og setninger
ABCD AC is equal ADDITIONAL PROPOSITION angle ACB angle BAC angles ABC anharmonic arc ABC bisected centre of similitude chord circle ABC coincide Constr Coroll cut the circle describe a circle diagonal diameter draw equal angles equal circles equal to CD equiangular equimultiples Euclid EXERCISES exterior angle given circle given point given straight line given triangle greater harmonic range hypotenuse inscribed intersect Let ABC meet middle points opposite sides pair parallel parallelogram pencil pentagon perpendicular polygon PROOF Prop PROPOSITION 14 Ptolemy's Theorem quadrilateral radical axis radius rectangle contained required to prove respectively rhombus right angles shew sides BC Similarly square on AC straight line &c straight line drawn straight line joining subtend tangent theorem triangle ABC triangle DEF triangles are equal twice the rectangle vertices Wherefore
Populære avsnitt
Side 59 - Any two sides of a triangle are together greater than the third side.
Side 7 - An angle less than a right angle is called an acute angle; an angle greater than a right angle and less than two right angles is called an obtuse angle.
Side 68 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 144 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...
Side 376 - To find a mean proportional between two given straight lines. Let AB, BC be the two given straight lines ; it is required to find a mean proportional between them. Place AB, BC in a straight line, and upon AC describe the semicircle ADC, and from the point B draw (9.
Side 135 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 76 - ... the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Side 305 - To inscribe, an equilateral and equiangular pentagon in a given circle. Let ABCDE be the given circle. It is required to inscribe an equilateral...
Side 424 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.
Side 248 - If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other. Let the two straight lines AC, BD, within the circle ABCD, cut one another in the point E : the rectangle contained by AE, EC is equal to the rectangle contained by BE, ED.