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 28.
Σελίδα 6
... interior angles on the same side of it , taken together , less than two right angles , these straight lines , being continually produced , shall at length meet upon that side on which are the angles which are less than two right angles ...
... interior angles on the same side of it , taken together , less than two right angles , these straight lines , being continually produced , shall at length meet upon that side on which are the angles which are less than two right angles ...
Σελίδα 16
... interior opposite angles . The Let A B C be a triangle , and let its side B C be produced to D. exterior angle ACD is greater than either of the interior opposite angles CBA , BAC . Bisect ( I. 10 ) A C in E , join BE and produce it to ...
... interior opposite angles . The Let A B C be a triangle , and let its side B C be produced to D. exterior angle ACD is greater than either of the interior opposite angles CBA , BAC . Bisect ( I. 10 ) A C in E , join BE and produce it to ...
Σελίδα 17
... interior and opposite angle ABC . To each of these unequals , add the angle ACB . Therefore the two angles ACD , ACB , are greater ( Ax . 4 ) than the two angles ABC , ACB . But the two angles ACD , ACB are together equal ( I. 13 ) to ...
... interior and opposite angle ABC . To each of these unequals , add the angle ACB . Therefore the two angles ACD , ACB , are greater ( Ax . 4 ) than the two angles ABC , ACB . But the two angles ACD , ACB are together equal ( I. 13 ) to ...
Σελίδα 19
... interior and opposite angle CED ( I. 16 ) . And the exterior angle CEB of the triangle AB E is greater than its interior and opposite angle BAC ( I. 16 ) . But the angle BDC is greater than the angle CEB . Much more then is the angle ...
... interior and opposite angle CED ( I. 16 ) . And the exterior angle CEB of the triangle AB E is greater than its interior and opposite angle BAC ( I. 16 ) . But the angle BDC is greater than the angle CEB . Much more then is the angle ...
Σελίδα 23
... interior and opposite angle B CA ; which is impossible ( I. 16 ) . Therefore BC is not unequal to EF ; that is , BC is equal to E F. And AB is equal ( Hyp . ) to D E. Therefore the two sides A B , B C are equal to the two sides DE , EF ...
... interior and opposite angle B CA ; which is impossible ( I. 16 ) . Therefore BC is not unequal to EF ; that is , BC is equal to E F. And AB is equal ( Hyp . ) to D E. Therefore the two sides A B , B C are equal to the two sides DE , EF ...
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...