The Elements of EuclidLongmans, Green and Company, 1866 - 376 páginas |
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Página 1
... lies wholly in that superficies . VIII , A plane angle is the inclination of two lines to one another in a plane , which meet together , but are not in the same direction . B • IX . A plane rectilineal angle is the inclination THE ...
... lies wholly in that superficies . VIII , A plane angle is the inclination of two lines to one another in a plane , which meet together , but are not in the same direction . B • IX . A plane rectilineal angle is the inclination THE ...
Página 2
... meet together , but are not in the same straight line . N.B. When several angles are at one point B , any one of them is expressed by three letters , of which the letter that is at the vertex of the angle , that is , at the point in ...
... meet together , but are not in the same straight line . N.B. When several angles are at one point B , any one of them is expressed by three letters , of which the letter that is at the vertex of the angle , that is , at the point in ...
Página 5
... straight lines , being continually produced , shall at length meet , upon that side on which are the angles that are less than two right angles . PROPOSITION I. PROBLEM . To describe an equilateral triangle upon в 3 BOOK I. II. ...
... straight lines , being continually produced , shall at length meet , upon that side on which are the angles that are less than two right angles . PROPOSITION I. PROBLEM . To describe an equilateral triangle upon в 3 BOOK I. II. ...
Página 28
... meet either towards B , D , or A E / B towards A , C : Let them be produced and meet towards B , D , at the point G : Then GEF is a triangle , and its exterior angle AEF is greater than the interior and opposite angle EFG ( 1. 16 ) ...
... meet either towards B , D , or A E / B towards A , C : Let them be produced and meet towards B , D , at the point G : Then GEF is a triangle , and its exterior angle AEF is greater than the interior and opposite angle EFG ( 1. 16 ) ...
Página 29
Euclides. like manner , it may be demonstrated that they do not meet towards A , C : But ( Def . 35 ) those straight lines which , being produced ever so far both ways , do not meet , are parallel to one another : Therefore AB is ...
Euclides. like manner , it may be demonstrated that they do not meet towards A , C : But ( Def . 35 ) those straight lines which , being produced ever so far both ways , do not meet , are parallel to one another : Therefore AB is ...
Términos y frases comunes
AB² ABCD AC² AD² adjacent angles angle ABC angle ACB angle BAC angle equal base BC BC is equal centre chord circle ABC circumference diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle fore given circle given line given point given rectilineal given straight line gnomon hypotenuse inscribed intersection isosceles triangle join less Let ABC lines be drawn lines drawn meet multiple opposite angles parallel to BC parallelogram perpendicular plane polygon PROB produced proportionals Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment semicircle shew shewn square on AC tangents THEOR touches the circle triangle ABC twice the rectangle vertex Wherefore