A Sequel to the First Six Books of the Elements of Euclid Containing An Easy in
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), and . -. = constant, and OP . OQ, is constant (hyp. ) ; . '. The ratio of OP . OR : OP . OQ: is constant : hence the ratio of OR : OQ is constant. Let C be the centre of Y; join OC, CR, and draw QI> II to CR. Mw OR : OQ : : C]- : QD; . -. The ratio of CR : QD is constant, and CR is constant; . *. QD is constant. In like manner OD is constant ; . *. D is a given point; . *. The locus of Q is a 0, whose centre is the given point D, and whose radius is DQ.
Cor. 1. — The centre of inversion is t...he centre of similitude of the original circle Y, and its inverse.
Cor. 2. — The circle Y, its inverse, and the circle of inversion are coaxal. Por if the O Y he cut in any point by the O of inversion, the O inverse to Y will pass through that point.
Prop. 2. — If two circles^ or a line and a circle, touch each other, their inverses will also touch each other.
Dem. — If two ©s, or a line and a O touch each other, they have two consecutive points common ; hence their inverses will have two consecutive points common, and therefore they touch each other.
What to read after A Sequel to the First Six Books of the Elements of Euclid Containing An Easy in?
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To quickly assess the difficulty of the text, read a short excerpt:
), and . -. = constant, and OP . OQ, is constant (hyp. ) ; . '. The ratio of OP . OR : OP . OQ: is constant : hence the ratio of OR : OQ is constant. Let C be the centre of Y; join OC, CR, and draw QI> II to CR. Mw OR : OQ : : C]- : QD; . -. The ratio of CR : QD is constant, and CR is constant; . *. QD is constant. In like manner OD is constant ; . *. D is a given point; . *. The locus of Q is a 0, whose centre is the given point D, and whose radius is DQ.
Cor. 1. — The centre of inversion is t...he centre of similitude of the original circle Y, and its inverse.
Cor. 2. — The circle Y, its inverse, and the circle of inversion are coaxal. Por if the O Y he cut in any point by the O of inversion, the O inverse to Y will pass through that point.
Prop. 2. — If two circles^ or a line and a circle, touch each other, their inverses will also touch each other.
Dem. — If two ©s, or a line and a O touch each other, they have two consecutive points common ; hence their inverses will have two consecutive points common, and therefore they touch each other.
What to read after A Sequel to the First Six Books of the Elements of Euclid Containing An Easy in?
You can find similar books in the "Read Also" column, or choose other free books by Casey John to read onlineMoreLess
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