Proposition XVIII.
IF(b) 1.1 4. Quantities are Proportional, either continuedly or dircretely, the Product of the Extremes is equal to the Product of the Means.
Mathesis enucleata, or, The elements of the mathematicks by J. Christ. Sturmius ; made English by J.R. and R.S.S.
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- Title
- Mathesis enucleata, or, The elements of the mathematicks by J. Christ. Sturmius ; made English by J.R. and R.S.S.
- Author
- Sturm, Johann Christophorus, 1635-1703.
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- London :: Printed for Robert Knaplock and Dan. Midwinter and Tho. Leigh,
- 1700.
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- Mathematics -- Early works to 1800.
- Geometry -- Early works to 1800.
- Algebra -- Early works to 1800.
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http://name.umdl.umich.edu/A61912.0001.001
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"Mathesis enucleata, or, The elements of the mathematicks by J. Christ. Sturmius ; made English by J.R. and R.S.S." In the digital collection Early English Books Online 2. https://name.umdl.umich.edu/A61912.0001.001. University of Michigan Library Digital Collections. Accessed June 20, 2025.
Pages
Page 71
Demonstration.
Suppose one Continual Proportional, a, ea, e{powerof2}a, e{powerof3}a.
| Extremes e{powerof3}a | Means e{powerof2}a |
| a | ea |
| Prod. e{powerof3}aa = Prod. e{powerof3}aa. Q.E.D. |
SCHOLIUM.
ON this Theorem is founded the Rule of Three in Arithme∣tick; so called because having 3 Numbers, (2. 5. 8.) it finds an unknown fourth Proportional. For altho this fourth be, as we have said, unknown, yets its Product by 2 is known, because the same with the Product of the Means, 5 and 8. Wherefore the Rule directs to multiply the third by the second, that you may thereby obtain the Product of the Extremes: which divided by one of the Extremes, viz. the first, necessa∣rily gives the other, i. e. the fourth sought.
Notes
-
(b) 1.1
E••cl. 16 l. 6 & 19. l. 7.