The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 1
... magnitude . II . A line is length without breadth . III . The extremities of a line are points . IV . A straight line is that which lies evenly between its extreme points . ས . A superficies is that which hath only length and breadth ...
... magnitude . II . A line is length without breadth . III . The extremities of a line are points . IV . A straight line is that which lies evenly between its extreme points . ས . A superficies is that which hath only length and breadth ...
Page 7
... Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . X. Two straight lines cannot inclose a space . XI . All right angles are ...
... Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . X. Two straight lines cannot inclose a space . XI . All right angles are ...
Page 126
... magnitudes " of the same kind to one another , in respect " of quantity . " IV . Magnitudes are said to have a ratio to one an- other , when the less can be multiplied so as to exceed the other . V. The first of four magnitudes is said ...
... magnitudes " of the same kind to one another , in respect " of quantity . " IV . Magnitudes are said to have a ratio to one an- other , when the less can be multiplied so as to exceed the other . V. The first of four magnitudes is said ...
Page 127
... magnitudes is said to have the same ratio to the second , which the third has to the fourth , when any equimultiples what- soever of the first and third being taken , and any equimultiples whatsoever of the second and fourth ; if the ...
... magnitudes is said to have the same ratio to the second , which the third has to the fourth , when any equimultiples what- soever of the first and third being taken , and any equimultiples whatsoever of the second and fourth ; if the ...
Page 128
... magnitudes are 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 continual propor- tionals , the first is said to have to the fourth the ...
... magnitudes are 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 continual propor- tionals , the first is said to have to the fourth the ...
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