The Contents of the Fifth and Sixth Books of EuclidThe University Press, 1900 - 143 σελίδες |
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Σελίδα xviii
... produced so that if PQ be drawn parallel to OB to cut OA in Q , and if PR be drawn parallel to OA to cut OB in R , then the parallelogram PQOR may have a given area . SECTION X. PROPOSITIONS 56-63 . THE REMAINING IMPORTANT THEOREMS IN ...
... produced so that if PQ be drawn parallel to OB to cut OA in Q , and if PR be drawn parallel to OA to cut OB in R , then the parallelogram PQOR may have a given area . SECTION X. PROPOSITIONS 56-63 . THE REMAINING IMPORTANT THEOREMS IN ...
Σελίδα 7
... construct equimultiples of a parallelogram and its base . Let ABCD be a parallelogram standing on the base AB . D C K L M N A B E LL F G H Fig . 3 . On AB produced take any number of lengths BE , 19 ] 7 EUCLID , BOOKS V. AND VI .
... construct equimultiples of a parallelogram and its base . Let ABCD be a parallelogram standing on the base AB . D C K L M N A B E LL F G H Fig . 3 . On AB produced take any number of lengths BE , 19 ] 7 EUCLID , BOOKS V. AND VI .
Σελίδα 8
Euclid, Micaiah John Muller Hill. On AB produced take any number of lengths BE , EF , FG , GH each equal to AB , and through E , F , G , H draw parallels to BC cutting DC produced in K , L , M , N respectively . Then the parallelograms ...
Euclid, Micaiah John Muller Hill. On AB produced take any number of lengths BE , EF , FG , GH each equal to AB , and through E , F , G , H draw parallels to BC cutting DC produced in K , L , M , N respectively . Then the parallelograms ...
Σελίδα 38
... produced set off a length BK equal to r ( BA ) . Then draw KL parallel to BC cutting CD produced at L. Then it is known by Art . 19 that BKLC = r ( ABCD ) . On EF produced set off a length EM equal to s ( EF ) . Then draw MN parallel to ...
... produced set off a length BK equal to r ( BA ) . Then draw KL parallel to BC cutting CD produced at L. Then it is known by Art . 19 that BKLC = r ( ABCD ) . On EF produced set off a length EM equal to s ( EF ) . Then draw MN parallel to ...
Σελίδα 50
... produced through A as in Fig . 79 , and C is nearer to A than to B. If K > L , then E must fall between D and A , as in Fig . 80 , and C is further from A than from B. K L X E A B C Fig . 80 . The proofs for the cases K < L and K > L ...
... produced through A as in Fig . 79 , and C is nearer to A than to B. If K > L , then E must fall between D and A , as in Fig . 80 , and C is further from A than from B. K L X E A B C Fig . 80 . The proofs for the cases K < L and K > L ...
Άλλες εκδόσεις - Προβολή όλων
The Contents of the Fifth and Sixth Books of Euclid Euclid,Micaiah John Muller Hill Πλήρης προβολή - 1900 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD ABEF angle equal angles reciprocally proportional BCGE BCHD BEFG BEHC bisected BLNO centre circle corresponding sides cross-ratio cutting AC DÊE definition divided drawn perpendicular duplicate ratio ENUNCIATION EQPS equal angles equimultiples Euclid's EXAMPLE exhibited in Fig expressed by Fig fact exhibited four harmonic points four straight lines greater Hence by Prop Hence the triangles hypotenuse integer inversion kind locus mean proportional middle point parallel to BC parallelogram PQRST PROPOSITION Proposition 48 rA rB rA sC radical axis ratio compounded ratio of equality rect rectangle contained relative multiple scale required to prove respectively equal right angle segments shows the fact side BC side corresponding similar figures similar triangles similarly described square on AB square on AC supplementary angles tangents three magnitudes triangle ABC triangle DEF triangles are similar vertex
Δημοφιλή αποσπάσματα
Σελίδα 99 - IF two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals : the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.
Σελίδα xviii - 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 99 - Prove that similar triangles are to one another in the duplicate ratio of their homologous sides.
Σελίδα xvi - If the vertical angle of a triangle be bisected by a straight line which also cuts the base, the segments of the base shall have the same ratio which the other sides of the triangle have to one another...
Σελίδα 99 - ABC, DEF have one angle in the one equal to one angle in the other, viz. the angle BAC to the angle EDF, and the sides about...
Σελίδα xvi - In a right triangle, if a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Σελίδα 35 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth: or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth : or, if...
Σελίδα 84 - If they do not intersect, show that the radical axis is perpendicular to the line joining the centres of the circles...
Σελίδα 100 - If an 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 of the straight line bisecting the angle.
Σελίδα 80 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means.