The school Euclid: comprising the first four books, by A.K. Isbister1863 |
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Αποτελέσματα 1 - 5 από τα 34.
Σελίδα 13
... fall within the triangle ACB . D E A B F CONSTRUCTION Join the vertices C and D , and produce AC , AD to E , F. DEMONSTRATION Because in the triangle ACD , AC is assumed to be equal to AD , therefore the angles ECD , FDC upon the other ...
... fall within the triangle ACB . D E A B F CONSTRUCTION Join the vertices C and D , and produce AC , AD to E , F. DEMONSTRATION Because in the triangle ACD , AC is assumed to be equal to AD , therefore the angles ECD , FDC upon the other ...
Σελίδα 34
... falling upon two other straight lines , make the alternate angles equal to one another , then these two straight lines shall be parallel . ( References - Prop . 1. 16 ; def . 35. ) Let the straight line EF , which falls upon the 34 ...
... falling upon two other straight lines , make the alternate angles equal to one another , then these two straight lines shall be parallel . ( References - Prop . 1. 16 ; def . 35. ) Let the straight line EF , which falls upon the 34 ...
Σελίδα 35
Euclides Alexander Kennedy Isbister. Let the straight line EF , which falls upon the two straight lines , AB , CD , make the alternate angles , AEF , EFD , equal to one another . Then AB shall be parallel to CD . A E B Z F D CONSTRUCTION ...
Euclides Alexander Kennedy Isbister. Let the straight line EF , which falls upon the two straight lines , AB , CD , make the alternate angles , AEF , EFD , equal to one another . Then AB shall be parallel to CD . A E B Z F D CONSTRUCTION ...
Σελίδα 36
... falling upon two other straight lines , make the exterior angle equal to the interior and opposite , upon the same side of the line , or make the interior angles upon the same side , together equal ... fall 36 [ BOOK I. THE SCHOOL EUCLID .
... falling upon two other straight lines , make the exterior angle equal to the interior and opposite , upon the same side of the line , or make the interior angles upon the same side , together equal ... fall 36 [ BOOK I. THE SCHOOL EUCLID .
Σελίδα 37
... fall upon two parallel straight lines , then it makes the alternate angles equal to each other ; and the exterior angle equal to the interior and opposite angle upon the same side ; and likewise the two interior angles upon the same ...
... fall upon two parallel straight lines , then it makes the alternate angles equal to each other ; and the exterior angle equal to the interior and opposite angle upon the same side ; and likewise the two interior angles upon the same ...
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The School Euclid: Comprising the First Four Books, Chiefly from the Text of ... A. K. Isbister Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2009 |
Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent angles alternate angles angle ABC angle BAC angle BCD angle EDF angle equal base BC BC is equal bisect centre circle ABC constr CONSTRUCTION cuts the circle DEMONSTRATION describe a circle describe the circle diameter double equal angles equal straight lines equal to BC equiangular pentagon equilateral and equiangular equilateral triangle Euclid exterior angle Geography given circle given point given rectilineal angle given straight line given triangle gnomon greater inscribed interior and opposite isosceles triangle less Let ABC Let the straight Ludgate Hill opposite angles parallel parallelogram pentagon perpendicular post 8vo produced Q. E. D. PROP rectangle contained rectilineal figure References Prop References-Prop remaining angle right angles segment semicircle side BC square of AC straight line AC THEOREM touches the circle triangle ABC twice the rectangle
Δημοφιλή αποσπάσματα
Σελίδα 94 - A CONSTRUCTION For, if not let it fall otherwise, if possible, as FGDB; let F be the centre of the circle ABC, and G the centre of ADE. Join AF and AG. DEMONSTRATION Because two sides of a triangle are together greater than the third side therefore AG, GF, are greater than FA;
Σελίδα 17 - and they are adjacent angles. But, ' 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;' (def. 10) therefore each of the angles DCF, ECF, is a right angle. Wherefore, from the point C, in the straight line AB,
Σελίδα xvii - to the same two, and when the adjacent angles are equal, they are right angles. Prop. 32. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle; the angles made by this line with the line touching the circle, shall be
Σελίδα ii - at right angles to a given straight line, from a given point in the same. Prop. 13. The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Prop. 14. If, at a point in a straight line, two other straight lines,
Σελίδα 2 - XV. 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. XVL And this point is called the centre of the circle.
Σελίδα ix - 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 of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Σελίδα 118 - (i. 32) and when the adjacent angles are equal, they are right angles, (i. def. 10.) PROP. XXXII. —THEOREM. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle; then the angles made by this line with the line
Σελίδα iii - to four right angles. Prop. 16. If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles. Prop. 17. Any two angles of a triangle are together less than two right angles. Prop.
Σελίδα 47 - Wherefore, triangles, &c. QED PROP. XXXVIII THEOREM. Triangles upon equal bases and between the same parallels are equal to one another. (References — Prop. i. 31, 34, 36 ; ax. 7.) Let the triangles ABC, DEF, be on the equal bases BC, EF, and between the same parallels AD, BF. Then
Σελίδα 23 - two angles of a triangle are together less than two right angles. Then any two of its angles shall be together less than two right angles, A CONSTRUCTION Produce the side BC to D. DEMONSTRATION Because ACD is the exterior angle of the triangle ABC, therefore the angle ACD is greater than the interior and opposite angle