The Elements of Euclid for the Use of Schools and CollegesMacmillan, 1872 - 400 Seiten |
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Seite 134
... than that of the second , the multiple of the third is also greater than that of the fourth . 6. Magnitudes which have the same ratio are called proportionals . When four magnitudes are proportionals it is usually expressed by Book V.
... than that of the second , the multiple of the third is also greater than that of the fourth . 6. Magnitudes which have the same ratio are called proportionals . When four magnitudes are proportionals it is usually expressed by Book V.
Seite 135
... proportionals , the first is said to have to the fourth , the triplicate ratio of that which it has to the second , and so on , quadruplicate , & c . increasing the denomination still by unity , in any num- ber of proportionals ...
... proportionals , the first is said to have to the fourth , the triplicate ratio of that which it has to the second , and so on , quadruplicate , & c . increasing the denomination still by unity , in any num- ber of proportionals ...
Seite 136
... proportionals , so that they continue still to be proportionals . 13. Permutando , or alternando , by permutation or alternately ; when there are four proportionals , and it is inferred that the first is to the third , as the second is ...
... proportionals , so that they continue still to be proportionals . 13. Permutando , or alternando , by permutation or alternately ; when there are four proportionals , and it is inferred that the first is to the third , as the second is ...
Seite 145
... proportionals , they shall also be proportionals when taken inversely . Let A be to B as C is to D : then also , inversely , B shall be to A as D is to C. Take of B and D any equimul- tiples whatever E and F ; and of A and C any ...
... proportionals , they shall also be proportionals when taken inversely . Let A be to B as C is to D : then also , inversely , B shall be to A as D is to C. Take of B and D any equimul- tiples whatever E and F ; and of A and C any ...
Seite 154
... proportionals ; namely , as A is to B , so let C be to D , and E to F : as A is to B , so shall A , C , E together be to B , D , F together . G- H- K- A- C- E- B- D F L M- N Take of A , C , E any equimultiples whatever G , H , K ; and ...
... proportionals ; namely , as A is to B , so let C be to D , and E to F : as A is to B , so shall A , C , E together be to B , D , F together . G- H- K- A- C- E- B- D F L M- N Take of A , C , E any equimultiples whatever G , H , K ; and ...
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Häufige Begriffe und Wortgruppen
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC 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