WE first of all tried to make a literal Demonstration by using the quantity of the square IK as you have it expressed Prop. 2. and 3. and the quantity IN as it was com∣pounded of CI=ob+eb+CN= 〈 math 〉〈 math 〉, &c. but we found it very tedious in making only the squares of IN and In. Then for the surd quantity CN we substituted another, viz. m, and we produced the squares of IN and In as above, but we added the square of IK in its first value; and thus we obtain'd the squares KN and Kn, but in such terms, that the exact roots could not be extracted, but must be exhibited as surd quantities, and consequently we must make use of the rules belonging to them to find their sum or difference, which we laid down Cons. 3. Prop. 7. and Consect. Prop. 10. Lib. 1. which tho' it would succeed, yet would be full of trouble and tediousness. Therefore at length when we came to use those other terms which express the square IK, the business succeed∣ed as easie as we could wish, and that in a plain and easie way and no less pleasant, which I doubt not but will also be the opinion of the Reader, who shall compare this with other demonstrations of the same thing, which only lead indirectly to this truth, or with them, which de Witte has given us in E∣lem▪ Curvar. lin. p. m. 293. and 302. and which he thinks
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.
- Link to this Item
-
http://name.umdl.umich.edu/A61912.0001.001
- 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 June 21, 2025.
Pages
Page 189
easie and short enough in respect of others both of the ancients and moderns, and which we have reduced into this yet more distinct form, and accommodated to our schemes.
Preparation for the Hyperbola.
Make as
- CD to CN
- EE−CN
- DCM
- MCE
- NCI
- nCI.
Because therefore it will be by Consect. 7. Prop. 7. as □ CD to □ DNE, so the □ DIE to the □ IK.
And also by composition, as □ CD to
- □CD+□DNE
- i. e. □ CN per 9. lib I.
Therefore by a Syllepsis, as □ CD to the □ CN so
- □ CD + DIE
- i. e. □ CI
But also by the Hypothesis. as the □ CD to the □ CN so □ CI to □ CM. Therefore □ CM is = □ CN + DIE + □ IK.