The Elements of EuclidLongmans, Green and Company, 1866 - 376 sider |
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Side 172
... proportionals . When four magnitudes are proportionals , it is usually expressed by saying , the first is to the second as the third is to the fourth . VII . When of the equimultiples of four magnitudes ( 172 ...
... proportionals . When four magnitudes are proportionals , it is usually expressed by saying , the first is to the second as the third is to the fourth . VII . When of the equimultiples of four magnitudes ( 172 ...
Side 173
... proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . xI . When four magnitudes are continued propor- tionals , the first is said to have to the fourth the tripli- cate ratio of ...
... proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . xI . When four magnitudes are continued propor- tionals , the first is said to have to the fourth the tripli- cate ratio of ...
Side 174
... proportionals , so that they continue still to be proportionals : XIII . 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 to ...
... proportionals , so that they continue still to be proportionals : XIII . 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 to ...
Side 175
... proportionals when taken two and two of each rank , and it is inferred that the first is to the last of the first rank of magnitudes , as the first is to the last of the others . Of this there are the two following kinds , which arise ...
... proportionals when taken two and two of each rank , and it is inferred that the first is to the last of the first rank of magnitudes , as the first is to the last of the others . Of this there are the two following kinds , which arise ...
Side 183
... proportionals , they are proportionals also when taken inversely . If A be to B as C is to D , then also , inversely , B shall be to A as D to C. Then , Take of B , D , any equimultiples whatever , E , F , and of A , C , any ...
... proportionals , they are proportionals also when taken inversely . If A be to B as C is to D , then also , inversely , B shall be to A as D to C. Then , Take of B , D , any equimultiples whatever , E , F , and of A , C , any ...
Vanlige uttrykk og setninger
AB² ABCD AC² AD² adjacent angles angle ABC angle ACB angle BAC angle equal base BC BC is equal centre chord circle ABC circumference diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle fore given circle given line given point given rectilineal given straight line gnomon hypotenuse inscribed intersection isosceles triangle join less Let ABC lines be drawn lines drawn meet multiple opposite angles parallel to BC parallelogram perpendicular plane polygon PROB produced proportionals Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment semicircle shew shewn square on AC tangents THEOR touches the circle triangle ABC twice the rectangle vertex Wherefore