The Geometrical Lectures of Isaac Barrow
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C > N.* 17. Hence it may be proved that : — If there are any four Hnes HBH, GBG, FBF, EBE, cutting one another at B, and these are so related that, if any straight line DH is drawn in any manner parallel to a straight line BD, given in position, or if through a given point D any straight line DH is drawn, DG is always an arithmetical mean of the same order be- tween DH and DE, and DF is the geometrical mean of the same order ; then the lines GBG, FBF will touch one another.
For it is evident fr...om the preceding that the line GBG will lie wholly outside the line FBF.
18. Hence also (I mention it briefly in passing), the asymptotes, straight lines applying to many different kinds of hyperbolae, and curves of hyperbolic form, may be defined.!
Thus, let two straight lines VD, BD be given in position, and let AGB, VEI be two other straight lines; now, any straight line PG being drawn parallel to DB, let P^ be always an arithmetical mean of the same order between PG and PE, and let PF be the geometrical mean of the same order.
What to read after The Geometrical Lectures of Isaac Barrow?
You can find similar books in the "Read Also" column, or choose other free books by Barrow Isaac to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
C > N.* 17. Hence it may be proved that : — If there are any four Hnes HBH, GBG, FBF, EBE, cutting one another at B, and these are so related that, if any straight line DH is drawn in any manner parallel to a straight line BD, given in position, or if through a given point D any straight line DH is drawn, DG is always an arithmetical mean of the same order be- tween DH and DE, and DF is the geometrical mean of the same order ; then the lines GBG, FBF will touch one another.
For it is evident fr...om the preceding that the line GBG will lie wholly outside the line FBF.
18. Hence also (I mention it briefly in passing), the asymptotes, straight lines applying to many different kinds of hyperbolae, and curves of hyperbolic form, may be defined.!
Thus, let two straight lines VD, BD be given in position, and let AGB, VEI be two other straight lines; now, any straight line PG being drawn parallel to DB, let P^ be always an arithmetical mean of the same order between PG and PE, and let PF be the geometrical mean of the same order.
What to read after The Geometrical Lectures of Isaac Barrow?
You can find similar books in the "Read Also" column, or choose other free books by Barrow Isaac to read onlineMoreLess
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