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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Σελίδα 4
... parallel , are called trapeziums ; but if one opposite pair be parallel and the other pair not , the figure is called a trapezoid . XXXV . Parallel straight lines are such as are in EUCLID'S ELEMENTS .
... parallel , are called trapeziums ; but if one opposite pair be parallel and the other pair not , the figure is called a trapezoid . XXXV . Parallel straight lines are such as are in EUCLID'S ELEMENTS .
Σελίδα 5
Euclides Robert Wallace. XXXV . Parallel straight lines are such as are in the same plane , and which being produced ever so far both ways do not meet . The meaning of this definition is , that the space between the lines is always of ...
Euclides Robert Wallace. XXXV . Parallel straight lines are such as are in the same plane , and which being produced ever so far both ways do not meet . The meaning of this definition is , that the space between the lines is always of ...
Σελίδα 6
... parallel to the same straight line . " The number of axioms is in this book limited to twelve ; but Euclid has tacitly assumed the truth of various other axioms , which will be noticed in the sequel . PROP . I. PROBLEM . To describe an ...
... parallel to the same straight line . " The number of axioms is in this book limited to twelve ; but Euclid has tacitly assumed the truth of various other axioms , which will be noticed in the sequel . PROP . I. PROBLEM . To describe an ...
Σελίδα 23
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles A E F , EFD , equal to one another . Then A B shall be parallel to CD . For , if AB be not parallel to CD , AB and CD ...
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles A E F , EFD , equal to one another . Then A B shall be parallel to CD . For , if AB be not parallel to CD , AB and CD ...
Σελίδα 24
... parallel ( Def . 35 ) to one another . Therefore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. The angles AEF , EFD , are called alternate angles , or more properly , interior alternate angles , because they are ...
... parallel ( Def . 35 ) to one another . Therefore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. The angles AEF , EFD , are called alternate angles , or more properly , interior alternate angles , because they are ...
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...