The Elements of Euclid |
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Page 119
... fourth , when any equimultiples whatsoever of the first and third being ta- ken , and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is ...
... fourth , when any equimultiples whatsoever of the first and third being ta- ken , and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is ...
Page 120
... fourth . VI . Magnitudes which have the same ratio are called propor- tionals . N. B. When four magnitudes are proportionals , it is usually expressed by saying , the first is to the se- ' cond , as the third to the fourth . ' VII ...
... fourth . VI . Magnitudes which have the same ratio are called propor- tionals . N. B. When four magnitudes are proportionals , it is usually expressed by saying , the first is to the se- ' cond , as the third to the fourth . ' VII ...
Page 121
... fourth ; or that the first is to the third , as the second to the fourth ; as is shown in the 16th prop . of this 5th book . XIV . Invertendo , by inversion : when there are four proportionals , and it is inferred , that the second is ...
... fourth ; or that the first is to the third , as the second to the fourth ; as is shown in the 16th prop . of this 5th book . XIV . Invertendo , by inversion : when there are four proportionals , and it is inferred , that the second is ...
Page 122
... fourth . Prop . E , book 5 . XVIII . Ex æquali ( sc . distantia ) , or ex æquo , from equality of dis- tance ; when there is any number of magnitudes more than two , and as many others , so that they are proportionals when taken two and ...
... fourth . Prop . E , book 5 . XVIII . Ex æquali ( sc . distantia ) , or ex æquo , from equality of dis- tance ; when there is any number of magnitudes more than two , and as many others , so that they are proportionals when taken two and ...
Page 124
... fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second , that the third together with the sixth is of the fourth . D Let ...
... fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second , that the third together with the sixth is of the fourth . D Let ...
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Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore