Books 3-9The University Press, 1908 |
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Αποτελέσματα 1 - 5 από τα 36.
Σελίδα 46
... angle at the circumference , when the angles have the same circum- ference as base . Let ABC be a circle , let the angle BEC be an angle 5 at its centre , and the angle BAC an angle at the circumference , and let them have the same ...
... angle at the circumference , when the angles have the same circum- ference as base . Let ABC be a circle , let the angle BEC be an angle 5 at its centre , and the angle BAC an angle at the circumference , and let them have the same ...
Σελίδα 47
Euclid. Similarly then we can prove that the angle GEC is double of the angle EDC , 30 of which the angle GEB is ... BAC is half of the angle BDC ; and the sum of the angles BDG , GDF , FDC is double of any angle in the segment BEC ...
Euclid. Similarly then we can prove that the angle GEC is double of the angle EDC , 30 of which the angle GEB is ... BAC is half of the angle BDC ; and the sum of the angles BDG , GDF , FDC is double of any angle in the segment BEC ...
Σελίδα 48
... angle BEC . And Euclid has proved the first part of the proposition , namely that the angle BDC is double of the angle BAC . F Now , says Heron , BAC is any angle in the segment BAC , and therefore any angle in the segment BAC is half of ...
... angle BEC . And Euclid has proved the first part of the proposition , namely that the angle BDC is double of the angle BAC . F Now , says Heron , BAC is any angle in the segment BAC , and therefore any angle in the segment BAC is half of ...
Σελίδα 50
... angles in it : these also are equal to one another . Draw AF to the centre , and produce it to C , and join CE . Therefore the segment BADC is greater than a semicircle , and the angles in it BAC , BEC are equal , by the first case ...
... angles in it : these also are equal to one another . Draw AF to the centre , and produce it to C , and join CE . Therefore the segment BADC is greater than a semicircle , and the angles in it BAC , BEC are equal , by the first case ...
Σελίδα 52
... triangle ABC are equal to two ... angle BDC , for they are in the same segment BADC ; [ 111. 21 ] and the angle ACB is equal to the angle ADB , for they are in the same segment ADCB ; therefore the whole angle ADC is equal to the angles BAC ...
... triangle ABC are equal to two ... angle BDC , for they are in the same segment BADC ; [ 111. 21 ] and the angle ACB is equal to the angle ADB , for they are in the same segment ADCB ; therefore the whole angle ADC is equal to the angles BAC ...
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.