The elements of Euclid for the use of schools and colleges : comprising the first two books and portions of the eleventh and twelfth books; with notes and exercises . -maining angle DEB, [A :dom 3. In the same manner ij may be shewn that the angleCEB is equal lo the angle AED. Wherefore, if tico straight lines &c. Corollary 1. From this it is manifest that, if two straightlines cut one another, the angles which they make at thepoint where they cut, are together equal to four right angles. Corollary 2. And consequently, that all the angles madeby any number of straight lines meeting at o
The elements of Euclid for the use of schools and colleges : comprising the first two books and portions of the eleventh and twelfth books; with notes and exercises . -maining angle DEB, [A :dom 3. In the same manner ij may be shewn that the angleCEB is equal lo the angle AED. Wherefore, if tico straight lines &c. Corollary 1. From this it is manifest that, if two straightlines cut one another, the angles which they make at thepoint where they cut, are together equal to four right angles. Corollary 2. And consequently, that all the angles madeby any number of straight lines meeting at one point, aretogether equal to four right angles. PROPOSITION 16. one side of a triangle he produced, the exterior angleshall he greater than either of the interior opposite angles. Let ABC be a triangle, and let one side BC be pro-fluced to D : the exterior angle A CD shall be greater thaneither of the interior opposite angles CBA, BAC Bisect AC at E, [L 10. join BE and produce it to F, making EF equal to EB, [I. join FC Because AE is equal to EC, and BE to EF ; [ two sides AE, EB are equal to the two sides CE, to each ;. BOOK I. 16, 17. 21 and the angle AEB is eqnal to the angle CEF,because they are opposite ver-tical angles; [I. the triangle AEBis equal to the triangle CEF,and the remaining angles tothe remaining angles, each toeach, to which the equal sidesare opposite; [I. the angle BAE isequal to the angle the angle ECD is greaterthan the angle ECF. \_Axiom the angle ACD is greater than the angleBAR. In the same manner if 56be bisected, and the side <4Cbe produced to Gy it may be shewn that the angle BCQ^ythat is the angle ACD^ is greater than the angle ABC, [, Wherefore, if one side &c. PROPOSITION 17. two angles of a triangle are together less than tuJOright angles. Let ABC be a triangle: any two of its angles aretogether less than two right angles. Produce BC to D.
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Keywords: ., bookcentury1800, booksubjectgeometry, booksubjectmathematicsgree
