Elements of geometry and trigonometry . + =^ (AI + CI).BD=, we «hall have + 113 M PROBLEMS RELATING TO THE FOURTH BOOK. PROBLEM I. To divide a given straight line into any number of equal parts,or into parts proportional to given lines. First, Let it be proposed to divide the lineAB into five equal parts. Through the ex-tremity A, draw the indefinite straight lineAG ; and taking AC of any magnitude, applyit five times upon AG ; join the last pointof division G, and the extremity B, by thestraight line GB ; then draw CI parallel to _GB : AI will be
Elements of geometry and trigonometry . + =^ (AI + CI).BD=, we «hall have + 113 M PROBLEMS RELATING TO THE FOURTH BOOK. PROBLEM I. To divide a given straight line into any number of equal parts,or into parts proportional to given lines. First, Let it be proposed to divide the lineAB into five equal parts. Through the ex-tremity A, draw the indefinite straight lineAG ; and taking AC of any magnitude, applyit five times upon AG ; join the last pointof division G, and the extremity B, by thestraight line GB ; then draw CI parallel to _GB : AI will be the fifth part of the line pAB ; and thus, by applying AI five times ^-upon AB, the line AB will be divided intofive equal parts. For, since CI is parallel to GB, the sides AG, AB, are cutproportionally in C and I (Prop, XV.). But AC is the fifthpart of AG, hence AI is the fifth part of AB, Secondly. Let it be pro-posed to divide the line ABinto parts proportional tothe given lines P, Q, A. draw the indefi-nite line AG ; make AC =P, CD=Q, DErrR; jointhe extremities E and B ;and through the points C, D, draw CI,
Size: 1285px × 1945px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
