Books 3-9The University Press, 1908 |
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Side 7
... Similarly we can prove that neither is any other point except F. Therefore the point F is the centre of the circle ABC . PORISM . From this it is manifest that , if in a circle a straight line cut a straight line into two equal parts ...
... Similarly we can prove that neither is any other point except F. Therefore the point F is the centre of the circle ABC . PORISM . From this it is manifest that , if in a circle a straight line cut a straight line into two equal parts ...
Side 16
... similarly substitutes as the criterion the angle subtended at the centre , but gives as his reason that the words " nearer " and " more remote " in Euclid's enunciation are scarcely clear enough without some definition of the sense in ...
... similarly substitutes as the criterion the angle subtended at the centre , but gives as his reason that the words " nearer " and " more remote " in Euclid's enunciation are scarcely clear enough without some definition of the sense in ...
Side 19
... Similarly we can prove that DL is also less than DH ; therefore DG is least , while DK is less than DL , and DL than DH . I say also that only two equal straight lines will fall from the point D on the circle , one on each side of the ...
... Similarly we can prove that DL is also less than DH ; therefore DG is least , while DK is less than DL , and DL than DH . I say also that only two equal straight lines will fall from the point D on the circle , one on each side of the ...
Side 20
... Similarly E lies further than Y from the foot of the same perpendicular . E M Heron deals with lines on opposite sides of the diameter through the external point in a manner similar to that adopted in his previous note . For the case ...
... Similarly E lies further than Y from the foot of the same perpendicular . E M Heron deals with lines on opposite sides of the diameter through the external point in a manner similar to that adopted in his previous note . For the case ...
Side 22
... Similarly we can prove that neither is any other point except D ; therefore the point D is the centre of the circle ABC . Q. E. D. " On this Todhunter correctly points out that the point E might be supposed to fall within the angle ADC ...
... Similarly we can prove that neither is any other point except D ; therefore the point D is the centre of the circle ABC . Q. E. D. " On this Todhunter correctly points out that the point E might be supposed to fall within the angle ADC ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 37 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Side 234 - Prove that similar triangles are to one another in the duplicate ratio of their homologous sides.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.