...AB and CD arc A & B divided proportionally at E and F if AB : AE = CD : C F. ~ F THEORBH XLIX. 171. A line parallel to one side of a triangle divides the other two sides proportionally. Let DE be parallel to side BC of triangle ABC. AB AC To prove that .-p =...

...Cor. Parallelograms or triangles of the same altitude are to one another as their bases. Prop. 107. A line parallel to one side of a triangle divides the other two sides proportionally. The two triangles thus formed have their corresponding sides proportional....

...draw EG II to DF. CONCLUSION. FG is the fourth proportional required. QEF PROOF. AD : DE = AF : FG. " A line parallel to one side of a triangle divides the other two sides proportionally." § 340 Substituting m, n, and p for AD, DE, and AF respectively, m:n=jo:FG....

...Third Book is reached? The same objections apply to the ordinary demonstration of the proposition that a line parallel to one side of a triangle divides the other two sides proportionally. There are the same doubtful variables and the difficulty of comprehending...

...draw EG II to DF. CONCLUSION. FG is the fourth proportional required. QEF PROOF. AD : DE = AF : FG. " A line parallel to one side of a triangle divides the other two sides proportionally." § 340 Substituting m, n, and p for AD, DE, and AF respectively, m : n =...

...understood that in the following geometrical propositions and demonstrations, the foregoing interpretation is implied in multiplication and division involving...and LB are commensurable. There exists a common unit ____ of measure of AL and LB (238). c Suppose this is contained 9 times in AL and 5 times in LB. Then,...

...understood that in the following geometrical propositions and demonstrations, the foregoing interpretation is implied in multiplication and division involving...ABC and line LM A II to BC. To Prove: AL : LB = AM : JfC. Proof: I. If the parts AL and LB are commensurable. There exists a common unit of measure of...

...extremes. The symbol \ expresses square root. 268. The truth of the following theorems* has been shown : 1. A line parallel to one side of a triangle divides the other two sides into corresponding parts having equal ratios. 2. A line bisecting an angle of a triangle...

...— nn Ex. 246. Given a • x = x : a — x, to find the value of x. PROPOSITION XIII. THEOREM. 340. A line parallel to one side of a triangle divides the other sides proportionally. C Proof. CASK I. When DA and CD are commensurable. Let CFbea common measure of CD and...

...also "Approximation of Values of Irrational Numbers," First-Year Mathematics, p. 295). COROLLARY I A line parallel to one side of a triangle divides the other two sides proportionally. Prove Proposition IV for Fig. 97. Bl 7 x FIG. 97 PROPOSITION V Theorem: //...