The Elements of geometry; or, The first six books, with the eleventh and twelfth, of Euclid, with corrections, annotations, and exercises, by R. Wallace. Cassell's ed1855 |
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Αποτελέσματα 1 - 5 από τα 98.
Σελίδα
... proved and abridged as the nature of the reasoning and the consistency of the argument will allow . The above - mentioned simplifications , amendments , and additions , and other improvements which will be found on perusal , have been ...
... proved and abridged as the nature of the reasoning and the consistency of the argument will allow . The above - mentioned simplifications , amendments , and additions , and other improvements which will be found on perusal , have been ...
Σελίδα 7
... proved that CA is equal to AB . Therefore the two straight lines CA , CB , are each of them equal to AB . But things which are equal to the same thing are equal ( Ax . 1 ) to one another . Therefore CA is equal to CB . Wherefore the ...
... proved that CA is equal to AB . Therefore the two straight lines CA , CB , are each of them equal to AB . But things which are equal to the same thing are equal ( Ax . 1 ) to one another . Therefore CA is equal to CB . Wherefore the ...
Σελίδα 9
... proved to coincide with the point E. Therefore the base B C shall coincide with the base EF . For , the point B coinciding with the point E , and the point C with the point F , if the base BC does not coincide with the base E F , the ...
... proved to coincide with the point E. Therefore the base B C shall coincide with the base EF . For , the point B coinciding with the point E , and the point C with the point F , if the base BC does not coincide with the base E F , the ...
Σελίδα 10
... proved to be equal to the angle CG B. Wherefore the two triangles BFC , CGB , are equal ( I. 4 ) , and their remaining angles are equal , each to each , viz . , those to which the equal sides are opposite . Therefore the angle FBC is ...
... proved to be equal to the angle CG B. Wherefore the two triangles BFC , CGB , are equal ( I. 4 ) , and their remaining angles are equal , each to each , viz . , those to which the equal sides are opposite . Therefore the angle FBC is ...
Σελίδα 11
... proved that_the_angle BDC is greater than the angle BCD . Therefore , the angle BDC is both equal to , and greater than the angle BCD , which is impossible . The third case , in which the vertex of one triangle is upon a side of the ...
... proved that_the_angle BDC is greater than the angle BCD . Therefore , the angle BDC is both equal to , and greater than the angle BCD , which is impossible . The third case , in which the vertex of one triangle is upon a side of the ...
Άλλες εκδόσεις - Προβολή όλων
The Elements of geometry; or, The first six books, with the eleventh and ... Euclides Πλήρης προβολή - 1881 |
The Elements of Geometry: Or, the First Six Books, with the Eleventh and ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle DEF angle EDF base BC bisected centre circle ABC circumference cone cylinder described diagonal diameter draw duplicate ratio equal angles equal Ax equal Const equiangular equimultiples Euclid ex æquali Exercise exterior angle fore given straight line gnomon homologous sides inscribed join less meet multiple opposite angle parallelogram parallelogram AC parallelopiped pentagon perpendicular polygon prism produced proposition Q. E. D. PROP reciprocally proportional rectangle contained rectilineal figure remaining angle right angles segment similar triangles solid angle sphere squares of AC straight line drawn straight lines A B THEOREM third three plane angles three straight lines triangle ABC triangle DEF triplicate ratio twice the rectangle vertex Wherefore whole angle
Δημοφιλή αποσπάσματα
Σελίδα 23 - 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.
Σελίδα 34 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Σελίδα 2 - 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.
Σελίδα 122 - 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 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Σελίδα 135 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.
Σελίδα 20 - PROBLEM. At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle.
Σελίδα 147 - Similar solid figures are such as have all their solid angles equal, each to each, and are contained by the same number of similar planes.
Σελίδα 37 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...