The Elements of EuclidLongmans, Green and Company, 1866 - 376 sider |
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Resultat 1-5 av 33
Side 5
... 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 enclose 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 enclose a space . XI . All right angles are ...
Side 172
... 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 to have ...
... 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 to have ...
Side 173
... 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 continued propor- tionals , the first is said to have to the fourth the tripli ...
... 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 continued propor- tionals , the first is said to have to the fourth the tripli ...
Side 174
... magnitude of proportionals , so that they continue still to be proportionals : XIII . Permutando , or alternando , by permutation or alternately ; when there are ... magnitudes more than two , and as many others , 174 EUCLID'S ELEMENTS .
... magnitude of proportionals , so that they continue still to be proportionals : XIII . Permutando , or alternando , by permutation or alternately ; when there are ... magnitudes more than two , and as many others , 174 EUCLID'S ELEMENTS .
Side 175
... magnitudes , are equal to one another . II . Those magnitudes , of which the same or equal magnitudes are equimultiples , are equal to one another . III . A multiple of a greater magnitude is greater than the same multiple of a less ...
... magnitudes , are equal to one another . II . Those magnitudes , of which the same or equal magnitudes are equimultiples , are equal to one another . III . A multiple of a greater magnitude is greater than the same multiple of a less ...
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