A Supplement to the Elements of EuclidG. and W. B. Whittaker, 1819 - 410 sider |
Inni boken
Resultat 6-10 av 46
Side 306
... given ratio : And it is easily shewn , ex absurdo , that no point which is out of the locus so determined , has the ... given directions , they shall be to one another in the same given ratio as the segments are , which they cut off from ...
... given ratio : And it is easily shewn , ex absurdo , that no point which is out of the locus so determined , has the ... given directions , they shall be to one another in the same given ratio as the segments are , which they cut off from ...
Side 316
... given point , either within or without a given rectilineal angle , to draw a straight line cutting off from the lines which con- tain the angle , segments , towards the summit of the angle , which shall be to one another in a given ratio ...
... given point , either within or without a given rectilineal angle , to draw a straight line cutting off from the lines which con- tain the angle , segments , towards the summit of the angle , which shall be to one another in a given ratio ...
Side 317
... given ratio . And the problem may be solved in the same manner , when the given point is within the given angle . PROP . XVI . 22. PROBLEM . To draw through a given point a straight line cutting the lines which contain a given ...
... given ratio . And the problem may be solved in the same manner , when the given point is within the given angle . PROP . XVI . 22. PROBLEM . To draw through a given point a straight line cutting the lines which contain a given ...
Side 318
... given ratio , and let BF cut AR in H ; then , ( E. 3. 6. ) since AH bisects the FAE , FH : HE :: AF : AE ; that is , FG is to GE in the given ratio . PROP . XVII . 23. THEOREM . If two trapeziums have an angle of the one equal to an ...
... given ratio , and let BF cut AR in H ; then , ( E. 3. 6. ) since AH bisects the FAE , FH : HE :: AF : AE ; that is , FG is to GE in the given ratio . PROP . XVII . 23. THEOREM . If two trapeziums have an angle of the one equal to an ...
Side 323
... given ratio to a given rectilineal figure . Find ( E. 14. 2. ) a square that shall be equal to the given rectilineal figure , and from its side , pro- duced if it be necessary , cut off ( E. 10. 6. ) a part , which shall be to the side ...
... given ratio to a given rectilineal figure . Find ( E. 14. 2. ) a square that shall be equal to the given rectilineal figure , and from its side , pro- duced if it be necessary , cut off ( E. 10. 6. ) a part , which shall be to the side ...
Andre utgaver - Vis alle
Vanlige uttrykk og setninger
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 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 subtend tangent THEOREM three given touch the circle trapezium vertex
Populære avsnitt
Side 310 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 198 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Side 366 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the...
Side 92 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 284 - And if the first have a greater ratio to the second, than the third has to the fourth, but the third the same ratio to the fourth, which the fifth has to the sixth...
Side 349 - Divide a straight line into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square on the other part.
Side 288 - Convertendo, by conversion ; when there are four proportionals, and it is inferred, that the first is to its excess above the second, as the third to its excess above the fourth.
Side 296 - ... line and the extremities of the base have the same ratio which the other sides of the triangle have to one...
Side 367 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Side 104 - In every triangle, the square of the side subtending any of the acute angles is less than the squares of the sides containing that angle by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular...