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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Σελίδα 17
... base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite ... base BC shall coincide with the base EF , because the point B coinciding with E , and C with F , if the bas BC does not ...
... base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite ... base BC shall coincide with the base EF , because the point B coinciding with E , and C with F , if the bas BC does not ...
Σελίδα 18
... base FC is equal b to the base GB , and the tri- angle AFC to the triangle AGB ; and the remaining angles of the one are equal to the remaining angles of the other , each to each , to which the equal sides are opposite ; viz . the angle ...
... base FC is equal b to the base GB , and the tri- angle AFC to the triangle AGB ; and the remaining angles of the one are equal to the remaining angles of the other , each to each , to which the equal sides are opposite ; viz . the angle ...
Σελίδα 19
... base DC is equal to the base AB , and the triangle DBC is equal to the triangle ACB , the less to the great- er : which is absurd . Therefore AB is not B unequal to AC , that is , it is equal to it . Wherefore , if two angles , & c ...
... base DC is equal to the base AB , and the triangle DBC is equal to the triangle ACB , the less to the great- er : which is absurd . Therefore AB is not B unequal to AC , that is , it is equal to it . Wherefore , if two angles , & c ...
Σελίδα 20
... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another , and likewise those which are terminated in the other extremity . Q. E. D. ...
... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another , and likewise those which are terminated in the other extremity . Q. E. D. ...
Σελίδα 21
... base BC coin- cides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different situation , as EG , FG ; then , upon the same base EF , and upon the same side of it , there can be two triangles ...
... base BC coin- cides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different situation , as EG , FG ; then , upon the same base EF , and upon the same side of it , there can be two triangles ...
Συχνά εμφανιζόμενοι όροι και φράσεις
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD 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 multiple opposite parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of BC rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 17 - 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 35 - 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 67 - 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 92 - 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 26 - 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 55 - 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 318 - 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 22 - 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 161 - 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 21 - 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.