The figures of Euclid with the enunciations, as printed in Euclid's Elements of plane geometry [book 1-4, 6] by W.D. Cooley1840 |
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Αποτελέσματα 1 - 5 από τα 9.
Σελίδα 11
... the other , but their bases unequal , the angle subtended by the greater base of the one , must be greater than the angle subtended by the less base of the other . да E PROP . XXVI . THEOR . If two triangles have BOOK I. 11.
... the other , but their bases unequal , the angle subtended by the greater base of the one , must be greater than the angle subtended by the less base of the other . да E PROP . XXVI . THEOR . If two triangles have BOOK I. 11.
Σελίδα 13
... the external equal to the internal and opposite angle on the same side ; and the two internal angles on the same side together equal to two right angles . E 1 G B A H D F PROP . XXX . THEOR . Straight lines which are BOOK I. 13.
... the external equal to the internal and opposite angle on the same side ; and the two internal angles on the same side together equal to two right angles . E 1 G B A H D F PROP . XXX . THEOR . Straight lines which are BOOK I. 13.
Σελίδα 32
... PROP . IV . THEOR . Two chords in a circle , intersecting in a point which is not the centre , cannot bisect each other . E F D PROP . V. B THEOR . If two circles intersect , they have not the same centre . E PROP . VI . THEOR . If two ...
... PROP . IV . THEOR . Two chords in a circle , intersecting in a point which is not the centre , cannot bisect each other . E F D PROP . V. B THEOR . If two circles intersect , they have not the same centre . E PROP . VI . THEOR . If two ...
Σελίδα 44
... E PROP . XXXIII . PROB . Upon a given straight line to describe a segment of a circle containing an angle equal to a given angle . F B PROP . XXXIV . PROB . To cut off from 44 EUCLID'S ELEMENTS .
... E PROP . XXXIII . PROB . Upon a given straight line to describe a segment of a circle containing an angle equal to a given angle . F B PROP . XXXIV . PROB . To cut off from 44 EUCLID'S ELEMENTS .
Σελίδα 59
... E PROP . XII . PROB . To find a fourth proportional to three given straight lines . A B C G H E F PROP . XIII . PROB . To find a mean proportional between two given straight lines . B PROP . XIV . THEOR . Equal parallelograms which have ...
... E PROP . XII . PROB . To find a fourth proportional to three given straight lines . A B C G H E F PROP . XIII . PROB . To find a mean proportional between two given straight lines . B PROP . XIV . THEOR . Equal parallelograms which have ...
Άλλες εκδόσεις - Προβολή όλων
The Figures of Euclid with the Enunciations, as Printed in Euclid's Elements ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
angle contained angle subtended bisect a given centre or circumference CHANCERY LANE COR.-Hence cutting line describe a circle divide a given E PROP equal angles reciprocally equal arches equal circles equal sides equal straight lines equal to four equi equilateral and equiangular EUCLID'S ELEMENTS external segment F B PROP F PROP finite straight line four straight lines given circle given finite straight given point given rectilinear angle given rectilinear figure given straight line given triangle half the line homologous sides inscribe an equilateral internal angles isosceles triangle line be bisected line be divided lines be drawn lines be proportional obtuse angle opposite angle parallelogram equal perpendicular point of contact points of section polygons PROB rectangle contained right angles side opposite side subtending Similar triangles spectively equal square of half straight line drawn straight line touches tangent THEOR three given straight touches a circle twice the rectangle whole line XXXIII
Δημοφιλή αποσπάσματα
Σελίδα 62 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Σελίδα 29 - In every triangle, the square of the side subtending any of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Σελίδα 57 - 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.
Σελίδα 55 - 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...
Σελίδα 58 - 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 26 - 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 in the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 54 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally ; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Σελίδα 56 - The sides about the equal angles of equiangular triangles are proportionals ; and those which are opposite to the equal angles are homologous sides, that is, are the antecedents or consequents of the ratios Let ABC, DCE, be equiangular triangles, having the angle ABC equal to the angle DCE, and the angle ACB to the angle DEC, and consequently (4.
Σελίδα 40 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.
Σελίδα 69 - IN right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar and similarly described figures upon the sides containing the right angle...