Schultze and Sevenoak's Plane Geometry

Schultze and Sevenoak's Plane Geometry

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1913 edition. Excerpt: ...sequence of equations. Hence Proof. a: b = c: d. (Hyp.).-. ad = be. (276).: ad + bd = be + bd. (Ax. 2).: d(a + b)=b(c + d) (Sub.).-. a + b: b = c + d: d. (279) Note. A much simpler proof, which, however, is more difficult to discover, is the following: Proof. combining, Proposition VII. Theorem 284. If four quantities are in proportion, they are in proportion by division, i.e. the difference between the first two terms is to the second term as the difference between the last two terms is to the fourth term. This method may be applied to Props. IV to IX. Ex. 769. Make an analysis of Prop. VII and derive a proof from it. (Similar to 283.) Ex. 770. Transform the following proportions so that only one term contains x. (a) 2:3 = 5-x: x. (?) 4: 3 = 2 + x: x. (6) 6: 7 = 2-x: x. (e) 7:5 = 3 + x: x. (c) a: 6 = 5--x: x. (/) a: b = 5 +x: x. Ex. 771. If x + y: y = 7: 3, find the ratio of a; and y. Ex. 772. If x--j/: y = 2: 3, find the ratio of x and y. Proposition VIII. Theorem 285. If four quantities are in proportion, they are in proportion by composition and division, i.e. the sum of the first two terms is to their difference as the sum of the last two terms is to their difference. Ex. 773. Make an analysis of Prop. VIII and derive a proof from it. (283) Ex. 774. Transform the following proportions so that only one term contains x. (a) 3: 2 = 5 + x: 5-x. (6) 5: 3 = 3 + x: 3-x. (c) a: b = 1 + X: 1--x. Ex. 775. If x + y: x--y = 12: 5, find the ratio of x to y. Ex. 776. If x + y: x--y = a.: b, find the ratio of x to y. Proposition IX. Theorem 286. In a series of equal ratios, the sum of any number of antecedents is to the sum of the corresponding consequents as any antecedent is to its consequent. Proposition X. Theorem 287. The products of the correspondishow more

Product details

  • Paperback | 58 pages
  • 189 x 246 x 3mm | 122g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236589815
  • 9781236589811