The Elements of EuclidDesilver, Thomas, 1838 - 416 páginas |
Dentro del libro
Resultados 1-5 de 100
Página 11
... bases , or third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to ... base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite ...
... bases , or third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to ... base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite ...
Página 12
... base BC shall coincide with the base EF , because the point B coinciding with E , and C with F , if the base BC does not coincide with the base EF , two straight lines would inclose a space , which is impossible . ( 10. Ax . ) Therefore the ...
... base BC shall coincide with the base EF , because the point B coinciding with E , and C with F , if the base BC does not coincide with the base EF , two straight lines would inclose a space , which is impossible . ( 10. Ax . ) Therefore the ...
Página 13
... base of the triangle ABC : and it has also been proved that the angle FBC is equal to the angle GCB , which are the an- gles upon the other side of the base . Therefore the angles at the base , & c . Q. E. D. COROLLARY . gular . Hence ...
... base of the triangle ABC : and it has also been proved that the angle FBC is equal to the angle GCB , which are the an- gles upon the other side of the base . Therefore the angles at the base , & c . Q. E. D. COROLLARY . gular . Hence ...
Página 14
... 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. ...
Página 15
... base BC coincides 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 that ...
... base BC coincides 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 that ...
Otras ediciones - Ver todas
Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC square of BC straight line AB straight line BC tangent THEOR triangle ABC triplicate ratio vertex wherefore
Pasajes populares
Página 34 - 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 at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Página 143 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical 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 on the straight line which bisects the angle.
Página 63 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Página 246 - 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.
Página 9 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 119 - 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.
Página 19 - 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.
Página 12 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.
Página 78 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Página 131 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.