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 66.
Σελίδα 4
... shown in the sequel . XXX . Of four - sided figures , a square is that which has all its sides equal , and all its angles right angles . This definition is redundant . If the general definition annexed to the 34th Prop . of this book be ...
... shown in the sequel . XXX . Of four - sided figures , a square is that which has all its sides equal , and all its angles right angles . This definition is redundant . If the general definition annexed to the 34th Prop . of this book be ...
Σελίδα 7
... shown that BC is equal to B G. Wherefore AL and BC are each of them equal to BG . And things that are equal to the same thing are equal ( Ax . 1 ) to one another . Therefore the straight line AL is straight line BC . Wherefore from the ...
... shown that BC is equal to B G. Wherefore AL and BC are each of them equal to BG . And things that are equal to the same thing are equal ( Ax . 1 ) to one another . Therefore the straight line AL is straight line BC . Wherefore from the ...
Σελίδα 9
... shown in the same manner , that the angles formed upon the other sides of the bases of the triangles would be equal , each to each . Exercise . If two squares have one side of the one equal to one side of the other , the squares are ...
... shown in the same manner , that the angles formed upon the other sides of the bases of the triangles would be equal , each to each . Exercise . If two squares have one side of the one equal to one side of the other , the squares are ...
Σελίδα 16
... shown that no other straight line but BD , can be in the same straight line with B C. Therefore BD is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. Corollary . If at a point in a straight line , two ...
... shown that no other straight line but BD , can be in the same straight line with B C. Therefore BD is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. Corollary . If at a point in a straight line , two ...
Σελίδα 18
... shown that AC is not equal to AB . Therefore the side AC is greater than the side AB . Wherefore the greater angle , & c . Q. E. D. Corollary . - One side of a triangle is greater than , equal to , or less than another , according as ...
... shown that AC is not equal to AB . Therefore the side AC is greater than the side AB . Wherefore the greater angle , & c . Q. E. D. Corollary . - One side of a triangle is greater than , equal to , or less than another , according as ...
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...