A Supplement to the Elements of EuclidG. and W. B. Whittaker, 1819 - 410 σελίδες |
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Σελίδα 281
... given ratio , the ratio of the sum of their antecedents to the sum of their consequents , shall be greater than that given ratio . Let the ratios ( A : B ) , ( C : D ) , ( E : F ) , & c . be equal to one another , and let each of ...
... given ratio , the ratio of the sum of their antecedents to the sum of their consequents , shall be greater than that given ratio . Let the ratios ( A : B ) , ( C : D ) , ( E : F ) , & c . be equal to one another , and let each of ...
Σελίδα 301
... ratio as the rectangles con- tained by the sides about equal angles in each . Let AC , DF , be two equiangular ... given , that are opposite to AB and DE , to meet AH and DK , in M and P , respectively . And , since ( hyp . ) the ...
... ratio as the rectangles con- tained by the sides about equal angles in each . Let AC , DF , be two equiangular ... given , that are opposite to AB and DE , to meet AH and DK , in M and P , respectively . And , since ( hyp . ) the ...
Σελίδα 303
... given ratio : And secondly , to find the locus of all the points , from each of which if two straight lines be drawn in like manner , they shall cut off from two given parts of the straight lines containing the given angle , segments ...
... given ratio : And secondly , to find the locus of all the points , from each of which if two straight lines be drawn in like manner , they shall cut off from two given parts of the straight lines containing the given angle , segments ...
Σελίδα 304
Daniel Cresswell. Let CAB be the given 2 ; let AK , AL . , be the two C Q M K L A P B B straight lines given in position ; and let AL be to AK in the given ratio : It is required , first , to find , within the ∠ CAB , the locus of all ...
Daniel Cresswell. Let CAB be the given 2 ; let AK , AL . , be the two C Q M K L A P B B straight lines given in position ; and let AL be to AK in the given ratio : It is required , first , to find , within the ∠ CAB , the locus of all ...
Σελίδα 305
... ratio as the given finite straight lines AK and AL , From CA cut off CE = AK , and from BA cut off BF = AL ; from C and B , draw ( E. 31. 1. ) CD parallel to AL , and BD parallel to AK , and let CD and BD meet in D ; likewise from E and ...
... ratio as the given finite straight lines AK and AL , From CA cut off CE = AK , and from BA cut off BF = AL ; from C and B , draw ( E. 31. 1. ) CD parallel to AL , and BD parallel to AK , and let CD and BD meet in D ; likewise from E and ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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 figure 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 opposite sides parallel to BC parallelogram pass perimeter polygon PROBLEM produced PROP rectangle contained 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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 296 - ... line and the extremities of the base have the same ratio which the other sides of the triangle have to one...
Σελίδα 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.
Σελίδα 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...