The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth BooksMacmillan, 1886 - 400 Seiten |
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Seite 134
... equimultiples whatever of the first and the third being taken , and any equimultiples whatever of the second and the fourth , if the multiple of the first be less than that of the second , the multiple of the third is also less than ...
... equimultiples whatever of the first and the third being taken , and any equimultiples whatever of the second and the fourth , if the multiple of the first be less than that of the second , the multiple of the third is also less than ...
Seite 135
... equimultiples of four magnitudes , taken as in the fifth definition , the multiple of the first is greater than the multiple of the second , but the multiple of the third is not greater than the multiple of the fourth , then the first ...
... equimultiples of four magnitudes , taken as in the fifth definition , the multiple of the first is greater than the multiple of the second , but the multiple of the third is not greater than the multiple of the fourth , then the first ...
Seite 137
... Equimultiples of the same , or of equal magnitudes , are equal to one another . 2. Those magnitudes , of which the same or equal mag- nitudes are equimultiples , are equal to one another . 3. A multiple of a greater magnitude is greater ...
... Equimultiples of the same , or of equal magnitudes , are equal to one another . 2. Those magnitudes , of which the same or equal mag- nitudes are equimultiples , are equal to one another . 3. A multiple of a greater magnitude is greater ...
Seite 138
... equimultiples of as many , each of each ; whatever multiple any one of them is of its part , the same multiple shall all the first magni- tudes be of all the other . Let any number of magnitudes AB , CD be equimul- tiples of as many ...
... equimultiples of as many , each of each ; whatever multiple any one of them is of its part , the same multiple shall all the first magni- tudes be of all the other . Let any number of magnitudes AB , CD be equimul- tiples of as many ...
Seite 139
... equimultiples , these shall be equimultiples , the one of the second , and the other of the fourth . Let A the first be the same multiple of B BOOK V. 2 , 3 . 139.
... equimultiples , these shall be equimultiples , the one of the second , and the other of the fourth . Let A the first be the same multiple of B BOOK V. 2 , 3 . 139.
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Häufige Begriffe und Wortgruppen
ABCD angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC BC is equal bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore