# The Young Mathematician's Guide, by John Ward,

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1734 edition. Excerpt: ...C c 2 ' 'And late oLfind the I/alue of the unknown quantity, (a) in umhers. But every Aafected E uation, hath as many Root: (or rather Values of the unknown uantit ) either Real or Imaginary, as are the Dimenfions (viz. the ndex) of its highest Power; and therefore the Atantii) a, in this Equation, hath another Vetlue' either Affirmative or Negative; which may be thus found. The given Eauation is aa+g2a=4644, and its Root a=s4.' Let these two Equatians be made Equal or Eauated to o; bia. to' Nothing. 20; i-Algebga, -Part II. of the first Principles of Geometry, therefore lsha refer that Work to the next Part. Chap. 9. Of Numerttal Quelttons. _ 2 1 t _' Question 16. There are Two Numbers, the Sum of their Squares is 2 3 6 8; And the Greater of them is' in Proportion to the Less, As 6 To I. What are these Numbers? Question 17. There are TherexNutnbers in continuedPro. portion, the Sum of the Extreamsis 156, and the Mezn is 725 What are the Two. Extteanas? Question ' 18. There are Three Nurhbers in their Sum is 74, and the Sum of their Squares is 19245 What are those Numbers? 7 Question 19. There are Three Numbers in their Sum is 76; and if the Sum of the Extreams be Mulriplied into the Mean, that Product will be 1248; What are those Numbers? two Extreams. Therefore it must be ez-'zs-Viss-pzu. (See page 201. Question 20. There are Three Numbers in Arithmetical Progreffion, the First being Added to 'Twicevthe Second, and Three times the Third, their Sum will be 62; and the Sum of all their Squares is 275; What are those Number-s?, v Suppose 1 a, e, '_y in Aritbmetiml Progreffian. + y 2: 62. l And 2::: iZ: e-iy_7-=27\$ _7 The Question Theh 4 a+ytze Per sea I-Chap. 6. 2-5 5 2e+2y:62-2e 5-s-2 6 e-I-yzgl-e 6-e 7 y==31-2e 4.97 8 a::4e-3I fl-Ozss...