The Elements of EuclidDesilver, Thomas, 1838 - 416 sider |
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Side 256
Euclid Robert Simson. Euclid had given , has been deceived in applying what is manifest , when understood of magnitudes , unto ratios , viz . that a magnitude cannot be both greater and less than another . That those things which are equal ...
Euclid Robert Simson. Euclid had given , has been deceived in applying what is manifest , when understood of magnitudes , unto ratios , viz . that a magnitude cannot be both greater and less than another . That those things which are equal ...
Side 270
... given space ; or , which is the same thing , having given AB the sum of the sides of a rectangle , and the magnitude of it being likewise given , to find its sides . And the fourth problem is the same with this . To find the point N in the ...
... given space ; or , which is the same thing , having given AB the sum of the sides of a rectangle , and the magnitude of it being likewise given , to find its sides . And the fourth problem is the same with this . To find the point N in the ...
Side 272
... magnitude , that are neither similar nor equal , as shall be demon- strated after the notes on the 10th definition ... given no definition of equal figures , and it is certain he did not give this : for what is called the 1st def . of ...
... magnitude , that are neither similar nor equal , as shall be demon- strated after the notes on the 10th definition ... given no definition of equal figures , and it is certain he did not give this : for what is called the 1st def . of ...
Side 274
Euclid Robert Simson. PROP . I. PROBLEM . Three magnitudes , A , B , C being given , to find a fourth such , that every three shall be greater than the remaining one . Let D be the fourth : therefore D must be less than A , B , C to ...
Euclid Robert Simson. PROP . I. PROBLEM . Three magnitudes , A , B , C being given , to find a fourth such , that every three shall be greater than the remaining one . Let D be the fourth : therefore D must be less than A , B , C to ...
Side 285
... magnitudes which are proportionals taken two and two , as well as to three which are proportional to other three . COR . PROP . VIII . B. XII . The demonstration of this is imperfect , because it is not shown that the triangular ...
... magnitudes which are proportionals taken two and two , as well as to three which are proportional to other three . COR . PROP . VIII . B. XII . The demonstration of this is imperfect , because it is not shown that the triangular ...
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC square of BC straight line AB straight line BC tangent THEOR triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 34 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Side 143 - 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 63 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 246 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Side 9 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Side 119 - 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 19 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 12 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.
Side 78 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 131 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.