By Francis J. Grund
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Additional info 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
QUERY If two also are therefore, throughout, at an equal distance from each other of other parallel MI, and consequently might go on, and show that every per- I equal to and In precisely the same manner I MPI. RS can prove that OP to the angle c, in the triangle equal to the side MI, opposite to the equal angle is d, in the triangle to there- : each other XII. a third line, lohat relation 7 Fig. I. 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 ; ?
VVhenever we compare two things with regard to magnitude, and inquire how many times one is greater than the other, we determine the ratio which their these two things bear to each other. find out that the one greater than the other, is we way, we If, in this two, three, four, &,c. times say that these things are in the ratio of one to two, to three, to four, Sfc. : e. g. compare the fortunes of two persons, dne of If you whom is worth 810,000, and the other $20,000, you say, that Or if you their fortunes are in the ratio of one to two.
I. ) : in proportion to the sides BC ^Iso in proportion to the sides ABC of the triangle will and take the two If the sides AB AC and he, and ac, the three sides be in proportion to the three sides of the triangle ahe; therefore, any tioo sides of the first triangle will be in proportion to the two correspond- ing sides of the other triangle. Another important principle of geometrical pro- 4th. portions tions, is this: of which a ratio common to the a ivith the third, common with ratio and so on the ; the the second terms, which the the To sums will prove iljimplest easier to this, case we comprehend which we have just it, proportions only AC = aft AB ah AB = 6c BC.
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 by Francis J. Grund