Books 3-9The University Press, 1908 |
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Αποτελέσματα 6 - 10 από τα 35.
Σελίδα 229
... extremes be equal to that contained by the means , the four straight lines are proportional . [ VI . 16 ] Therefore , as A is to B , so is D to C. But B is equal to D ; therefore , as A is to B , so is B to C. Therefore etc. VI . 17 is ...
... extremes be equal to that contained by the means , the four straight lines are proportional . [ VI . 16 ] Therefore , as A is to B , so is D to C. But B is equal to D ; therefore , as A is to B , so is B to C. Therefore etc. VI . 17 is ...
Σελίδα 243
... extreme terms is greater than double the middle term . II . We now come to the alternative which substitutes a new proof for the second part of the proposition , making the whole proposition an immediate inference from one to which it ...
... extreme terms is greater than double the middle term . II . We now come to the alternative which substitutes a new proof for the second part of the proposition , making the whole proposition an immediate inference from one to which it ...
Σελίδα 267
... extreme and mean ratio . Let AB be the given finite straight line ; thus it is required to cut AB in extreme and mean ratio . On AB let the square BC be described ; and let there be applied to AC the parallelo- gram CD equal to BC and ...
... extreme and mean ratio . Let AB be the given finite straight line ; thus it is required to cut AB in extreme and mean ratio . On AB let the square BC be described ; and let there be applied to AC the parallelo- gram CD equal to BC and ...
Σελίδα 268
... extreme and mean ratio at E , and the greater segment of it is AE . Q. E. F. It will be observed that the construction in the text is a direct application of the preceding Prop . 29 in the particular case where the excess of the ...
... extreme and mean ratio at E , and the greater segment of it is AE . Q. E. F. It will be observed that the construction in the text is a direct application of the preceding Prop . 29 in the particular case where the excess of the ...
Σελίδα 282
... extremes ( cf. note on the following definition ) . The even - times even is then the number which has its halves ... extreme . It is such a number as , when once halved , leaves as quotient an odd number ; that is , it is of the form 2 ...
... extremes ( cf. note on the following definition ) . The even - times even is then the number which has its halves ... extreme . It is such a number as , when once halved , leaves as quotient an odd number ; that is , it is of the form 2 ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD angle ABC angle BAC antecedent Aristotle base bisected centre circle ABC circumference construction continued proportion corresponding sides cube number definition diameter drawn enunciation equal angles equiangular equimultiples Euclid Eutocius ex aequali four magnitudes geometrical geometrical progression given circle given straight line greater ratio greatest common measure Heiberg hypothesis Iamblichus joined less mean proportional numbers measures the number multiple multitude Nicomachus odd number parallel parallelogram pentagon polygon Porism prime number Proclus Prop proper fraction proposition PROPOSITION 13 proved rect rectangle rectangle contained rectilineal figure reductio ad absurdum remaining angle right angles segment semicircle similar and similarly similar plane numbers Simson solid numbers square number subtracted taken Theon Theon of Smyrna theorem touches the circle triangle ABC unit VIII δὲ καὶ πρὸς τὸ τοῦ
Δημοφιλή αποσπάσματα
Σελίδα 34 - EQUAL straight lines in a circle are equally distant from the centre ; and those which are equally distant from the centre, are equal to one another.
Σελίδα 65 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Σελίδα 37 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Σελίδα 234 - Prove that similar triangles are to one another in the duplicate ratio of their homologous sides.
Σελίδα 64 - From this it is manifest that if one angle of a triangle be equal to the other two it is a right angle, because the angle adjacent to it is equal to the same two ; (i.
Σελίδα 209 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Σελίδα 90 - EF at right angles (9. 1.) to AB, AC ; DF, EF produced meet one another : for, if they do not meet, they are parallel, wherefore AB, AC, which are at right angles to them, are parallel ; which is absurd : let them meet in F, and join FA ; also, if the point F be not in BC, join BF, CF : then, because AD is equal to DB, and DF common, and at right angles to AB, the base AF is equal (4.
Σελίδα 80 - In a given circle to place a straight line, equal to a given straight line which is not greater than the diameter of the circle. Let ABC be the given circle, and D the given straight line, not greater than the diameter of the circle.
Σελίδα 212 - ... be parallel to the remaining side of the triangle. Let DE be drawn parallel to BC, one of the sides of the triangle ABC : BD is to DA, as CE to EA. Join BE, CD ; Then the triangle BDE is equal to the triangle CDE*, * «.i.
Σελίδα 95 - In the same manner, it may be demonstrated that the straight lines EC, ED, are each of them equal to EA or EB ; therefore the four straight lines EA, EB, EC, ED, are equal to one another ; and the circle described from the centre E, at the distance of one of them, shall pass through the extremities of the other three, and be described about the square ABCD.