SOLƲTION.
1. Denomination. Make AB=a, BD=b, AC=x; then will BC=x+b.
2. Equation by the Pythagorick Theorem, 〈 math 〉〈 math 〉, viz. the two Squares of the Sides to the Square of the Hypothenusa.
Mathesis enucleata, or, The elements of the mathematicks by J. Christ. Sturmius ; made English by J.R. and R.S.S.
About this Item
- 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.
- Publication
- London :: Printed for Robert Knaplock and Dan. Midwinter and Tho. Leigh,
- 1700.
- Rights/Permissions
-
To the extent possible under law, the Text Creation Partnership has waived all copyright and related or neighboring rights to this keyboarded and encoded edition of the work described above, according to the terms of the CC0 1.0 Public Domain Dedication (http://creativecommons.org/publicdomain/zero/1.0/). This waiver does not extend to any page images or other supplementary files associated with this work, which may be protected by copyright or other license restrictions. Please go to http://www.textcreationpartnership.org/ for more information.
- Subject terms
- Mathematics -- Early works to 1800.
- Geometry -- Early works to 1800.
- Algebra -- Early works to 1800.
- Cite this Item
-
"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 May 17, 2024.
Pages
Page 18
3. Reduction. Substracting from both sides xx, you'l have 〈 math 〉〈 math 〉; and moreover by substracting also 〈 math 〉〈 math 〉; and dividing by 〈 math 〉〈 math 〉.
4. Effection or Geometrical Construction. Having described upon the given Base AB a Semi-circle, apply therein the given difference BD, and draw AD, whose Square is =aa−bb. Since this must be divided by 2b, make, as AE=2b to AD = 〈 math 〉〈 math 〉, so AD = 〈 math 〉〈 math 〉 to AC the Per∣pendicular sought. To which if you add CF=BD, you will have AF= to the Hypothenusa sought BC; which will come of course together with the whole Triangle sought, if the found Perpendicular AC be erected at right Angles on the given Base AB.
5. The Rule for Arithmetical Cases. From the square of the given Base substract the square of the given difference, and divide the Remainder by the double difference; and you'l have the Perpendicular sought. E. g. suppose the Base = 20 foot, and the difference between the Perpendicular and Hypothenu∣sa 10.