The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 127
... fourth , when any equimultiples what- soever of the first and third being taken , 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 what- soever of the first and third being taken , 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 128
... fourth the triplicate ratio of that which it has to the second , and so on , quadruplicate , & c . increas- ing the denomination still by unity , in any number of proportionals . Definition A , to wit of compound ratio . When there are ...
... fourth the triplicate ratio of that which it has to the second , and so on , quadruplicate , & c . increas- ing the denomination still by unity , in any number of proportionals . Definition A , to wit of compound ratio . When there are ...
Page 129
... fourth ; or that the first is to the third as the second to the fourth : as is shown in the 16th Prop . of this fifth 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 fifth book . XIV . Invertendo , by inversion ; when there are four proportionals , and it is inferred , that the second is ...
Page 130
... fourth . Prop . E. Book 5 . XVIII . Ex æquali ( sc . distantiâ ) , or ex æquo , from equa- lity of distance : when there is any number of magnitudes more than two , and as many others , such that they are proportionals when taken two ...
... fourth . Prop . E. Book 5 . XVIII . Ex æquali ( sc . distantiâ ) , or ex æquo , from equa- lity of distance : when there is any number of magnitudes more than two , and as many others , such that they are proportionals when taken two ...
Page 131
... fourth of the first rank , so is the third from the last to the last but two of the second rank ; and so on in a cross order : and the inference is as in the 18th definition . It is demonstrated in the 23rd Prop . of Book 5 . AXIOMS . I ...
... fourth of the first rank , so is the third from the last to the last but two of the second rank ; and so on in a cross order : and the inference is as in the 18th definition . It is demonstrated in the 23rd Prop . of Book 5 . AXIOMS . I ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole