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Read Online or Download An elementary treatise on geometry : simplified for beginners not versed in algebra. Part I, containing plane geometry, with its application to the solution of problems PDF

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Additional resources for An elementary treatise on geometry : simplified for beginners not versed in algebra. Part I, containing plane geometry, with its application to the solution of problems

Example text

AB, By is the length the distance of the point determined. 3e//y. If A from the line you imagine the perpendic- GEOMETftY. ular AD to ABC BE, 47 upon BC (Fig. ), or if the angle be obtuse (as in Fig. ) on be let fall its further extension there can be but one point in the line side of the perpendicular, from which a point A, AC as long as the line is of the preceding query) line AC, line BC, line BC, on drawn this to the (see consequence 6t:i therefore, by the length of the ; the point C, and thereby the whole of the third also determined.

A" Fig. n. D C -J jr^ They are parallel Q. How to each other. can you prove A. From the line CD this AB ; ? being parallel to AB, that every point in the line from the line F : CD and because is at EF is it follows an equal distance also parallel to AB, GEOMETRY. EF every point in the line from the line AB ; is an equal distance also at and therefore distances between the lines 33 CD Fig. ) and EF, or (in I^g. II] the differences between the equal distances, are equal that is, the lines CD, EF, are likewise equidistant ; and consequently parallel to each other.

Oblique lines, AD, AE, AF, successively greater, as they are perpendicular line AB than the are all ; the line ; line AE obtuse^ triangles that is, AE the line than the and so on. and become pendicular ; become line is the greater than the AD ; the line 0, p, r, AF &,c. successively greater, as the are more remote from the and, therefore, the sides which are successively opposite triangles AD For the angles ; ADE, AEF, &c. Sfc. , to these angles, in the ADE, AEF, AFN, must become greater with them.

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