The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner CorrectedConrad and Company, 1810 - 518 σελίδες |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 15
... straight line . Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre A , at the dis- tance AB , describe a the circle BCD , and from the centre B , at the distance BA ...
... straight line . Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre A , at the dis- tance AB , describe a the circle BCD , and from the centre B , at the distance BA ...
Σελίδα 17
... straight line AB upon DE ; the point B shall coincide with the point E , because AB is equal to DE ; and AB coinciding with DE , AC shall coincide with DF , be- cause the angle BAC is equal to the angle EDF ; wherefore also the point ...
... straight line AB upon DE ; the point B shall coincide with the point E , because AB is equal to DE ; and AB coinciding with DE , AC shall coincide with DF , be- cause the angle BAC is equal to the angle EDF ; wherefore also the point ...
Σελίδα 22
... segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B - draw BE at right angles to AB ; and because ABC is a straight line , the angle CBE is equal a to the 22 THE ...
... segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B - draw BE at right angles to AB ; and because ABC is a straight line , the angle CBE is equal a to the 22 THE ...
Σελίδα 23
... PROP . XIII . THEOR . THE angles which one straight line makes with another upon the one side of it , are either two right angles , or are together equal to two right angles . Book I. Let the straight line AB make with CD OF EUCLID . 23.
... PROP . XIII . THEOR . THE angles which one straight line makes with another upon the one side of it , are either two right angles , or are together equal to two right angles . Book I. Let the straight line AB make with CD OF EUCLID . 23.
Σελίδα 24
... straight line AB make with CD , upon one side of it , the angles CBA , ABD ; these are either two right angles , or are together equal to two right angles . For , if the angle CBA be equal to ABD , each of them is a A E A D B CD B C b ...
... straight line AB make with CD , upon one side of it , the angles CBA , ABD ; these are either two right angles , or are together equal to two right angles . For , if the angle CBA be equal to ABD , each of them is a A E A D B CD B C b ...
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ABCD altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABC circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple opposite parallel parallelogram perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of BC rectangle CB rectangle contained rectilineal figure right angles segment side BC similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 19 - FG; then, upon the same base EF, and upon the same side of it, there can be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in the other extremity: But this is impossible (i.
Σελίδα 37 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 69 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.
Σελίδα 94 - IF a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Σελίδα 28 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.
Σελίδα 57 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line, which is made of the whole and that part.
Σελίδα 320 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Σελίδα 24 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Σελίδα 163 - 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 23 - When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.