A Supplement to the Elements of EuclidJ. Deighton and Sons, Cambridge and G and W. B. Whittaker, Ave-Maria-Lane, 1819 - 410 sider |
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Side vi
... means of which the Geo- metry of this Supplement may be incor- porated , as it were , with that of Euclid , and the reading of both the treatises may be made to go on together . In the demonstrations of the propositions recourse has ...
... means of which the Geo- metry of this Supplement may be incor- porated , as it were , with that of Euclid , and the reading of both the treatises may be made to go on together . In the demonstrations of the propositions recourse has ...
Side 283
... the difference between the two means . PROP . IX . 10. THEOREM . If the first , together with the se- cond , of four magnitudes , have a greater ratio to the second , than the third , together with ELEMENTS OF EUCLID . 283.
... the difference between the two means . PROP . IX . 10. THEOREM . If the first , together with the se- cond , of four magnitudes , have a greater ratio to the second , than the third , together with ELEMENTS OF EUCLID . 283.
Side 288
... mean B , is greater than the excess of the mean B above the least , C. For it has been shewn that A : B :: A - B : B - C ; And ( hyp . ) A > B ; .. ( S. 1. 5. ) A - B > B - C . PROP . XVI . 18. THEOREM . If four magnitudes be propor ...
... mean B , is greater than the excess of the mean B above the least , C. For it has been shewn that A : B :: A - B : B - C ; And ( hyp . ) A > B ; .. ( S. 1. 5. ) A - B > B - C . PROP . XVI . 18. THEOREM . If four magnitudes be propor ...
Side 291
... mean . Let A , B , C , be three magnitudes which are pro- portionals : Then A + C > 2B . For ( hyp . and E. 6. def ... mean proportional , between two given magnitudes , is greater than a geometric mean proportional between the same two ...
... mean . Let A , B , C , be three magnitudes which are pro- portionals : Then A + C > 2B . For ( hyp . and E. 6. def ... mean proportional , between two given magnitudes , is greater than a geometric mean proportional between the same two ...
Side 298
... sides of an iso- sceles triangle , is a mean proportional between the base , and the half of the segment of the base , produced if necessary , which is cut off by a C BC be Der straight line drawn from the vertex 298 A SUPPLEMENT TO THE.
... sides of an iso- sceles triangle , is a mean proportional between the base , and the half of the segment of the base , produced if necessary , which is cut off by a C BC be Der straight line drawn from the vertex 298 A SUPPLEMENT TO THE.
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ABCD base BC bisect centre chord circle ABC circle described circumference constr decagon describe a circle describe the circle diameter distance divided double draw a straight draw E equi equiangular equilateral and equiangular F draw find a point finite straight line given circle given finite straight given point given ratio given square given straight line half hypotenuse inscribed isosceles less Let AB Let ABC lines be drawn magnitudes manifest manner meet the circumference number of equal number of sides parallel to BC parallelogram pass perimeter point G polygon PROBLEM produced PROP rectangle contained rectilineal figure remaining sides required to describe required to draw rhombus right angles segment semi-diameter straight line joining tangent THEOREM three given touch the circle trapezium vertex