Elements of geometry, based on Euclid, book i1877 |
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Σελίδα 33
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles A AEF , EFD , equal to one another . AB shall be parallel to CD . For if AB and CD be not parallel , they will meet if ...
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles A AEF , EFD , equal to one another . AB shall be parallel to CD . For if AB and CD be not parallel , they will meet if ...
Σελίδα 34
... CD , being produced , do not meet towards B , D. In like manner it may be shown that they do not meet towards A , C. But those straight lines in the same plane which being produced ever so far both ways do not meet are parallel ( Def ...
... CD , being produced , do not meet towards B , D. In like manner it may be shown that they do not meet towards A , C. But those straight lines in the same plane which being produced ever so far both ways do not meet are parallel ( Def ...
Σελίδα 35
... parallel to CD ( I. 27 ) . Therefore , if a straight line , & c . Q. E. D. Proposition 29. - Theorem . If a straight line fall upon two parallel straight lines , it makes the alternate angles equal to one another , and the exterior ...
... parallel to CD ( I. 27 ) . Therefore , if a straight line , & c . Q. E. D. Proposition 29. - Theorem . If a straight line fall upon two parallel straight lines , it makes the alternate angles equal to one another , and the exterior ...
Σελίδα 36
Edward Atkins. Hence AB and CD meet , and are parallel . .. 4AGH , not une- qual to 4 GHD . and < EGB = 4GHD , also Z BGH + Z GHD = two right angles . ZAGH or < AGK continually produced , shall at ... parallel to CD ( I. 27 ) 36 GEOMETRY .
Edward Atkins. Hence AB and CD meet , and are parallel . .. 4AGH , not une- qual to 4 GHD . and < EGB = 4GHD , also Z BGH + Z GHD = two right angles . ZAGH or < AGK continually produced , shall at ... parallel to CD ( I. 27 ) 36 GEOMETRY .
Σελίδα 37
Edward Atkins. Therefore AB is parallel to CD ( I. 27 ) . Therefore , straight lines , & c . Q. E. D. Proposition 31. - Problem . To draw a straight line through a given point , parallel to a given straight line . Let A be the given ...
Edward Atkins. Therefore AB is parallel to CD ( I. 27 ) . Therefore , straight lines , & c . Q. E. D. Proposition 31. - Problem . To draw a straight line through a given point , parallel to a given straight line . Let A be the given ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry, Based on Euclid, Βιβλίο 1 Edward Atkins Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Elements of Geometry, Based on Euclid, Βιβλίο 1 Edward Atkins Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2010 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal adjacent angles alternate angles angle ABC angle BAC angle BCD angle contained angle EDF angle EGB angle GHD angles BGH angles CBE angles equal bisect centre cloth Const describe the circle diagonal equal sides equal to BC equal triangles equilateral triangle exterior angle Fcap four right angles GHD Ax given point given rectilineal angle given straight line given triangle gram HENRY EVERS interior and opposite isosceles triangle join less Let ABC LL.D meet opposite angles parallel straight lines parallel to BC parallelogram ABCD perpendicular Post 8vo PROOF PROOF.-Because Q. E. D. Proposition rectilineal figure remaining angle right angles Ax side BC sides are opposite sides equal square described square GB third angle trapezium triangle ABC triangle DEF WILLIAM COLLINS
Δημοφιλή αποσπάσματα
Σελίδα 23 - 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 33 - 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 43 - Parallelograms upon the same base, and between the same parallels, are equal to one another.
Σελίδα 15 - The angles at the base of an Isosceles triangle are equal to one another ; and if the equal sides be produced, the angles upon the other side of the base shall also be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC...
Σελίδα 11 - Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another.
Σελίδα 37 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Σελίδα 41 - ... together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 15 - J which the equal sides are opposite, shall be equal, each to each, viz. the angle ABC to the angle DEF, and the angle ACB to DFE.
Σελίδα 55 - IF the square described upon one of 'the sides of a triangle be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Σελίδα 24 - If, at a point in a straight line, two other straight lines, on the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.