PROPOSITION XXVI. THEOREM.
A Parallelepipedon is divided into Two equally, by a Diagonal Plane.
Let the Parallelepipedon AB be divi∣ded
The elements of Euclid, explained and demonstrated in a new and most easie method with the uses of each proposition in all the parts of the mathematicks / by Claude Francois Milliet D'Chales, a Jesuit ; done out of French, corrected and augmented, and illustrated with nine copper plates, and the effigies of Euclid, by Reeve Williams ...
About this Item
- Title
- The elements of Euclid, explained and demonstrated in a new and most easie method with the uses of each proposition in all the parts of the mathematicks / by Claude Francois Milliet D'Chales, a Jesuit ; done out of French, corrected and augmented, and illustrated with nine copper plates, and the effigies of Euclid, by Reeve Williams ...
- Author
- Dechales, Claude-François Milliet, 1621-1678.
- Publication
- London :: Printed for Philip Lea ...,
- 1685.
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- Subject terms
- Geometry -- Early works to 1800.
- Mathematical analysis.
- Cite this Item
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"The elements of Euclid, explained and demonstrated in a new and most easie method with the uses of each proposition in all the parts of the mathematicks / by Claude Francois Milliet D'Chales, a Jesuit ; done out of French, corrected and augmented, and illustrated with nine copper plates, and the effigies of Euclid, by Reeve Williams ..." In the digital collection Early English Books Online 2. https://name.umdl.umich.edu/A38722.0001.001. University of Michigan Library Digital Collections. Accessed May 1, 2024.
Pages
Page 339
by the Plane CD, drawn from one Angle to the other: I say that it divideth the same into Two equally Let the Line EA, be supposed to be divided into as many parts as one listeth; and that from each, one hath drawn as many Planes parallel to the Base AF; each of those Planes is a Parallelogram equal to the Base AF (by the 24th.)
Demonstration. All the Parallelograms which can be drawn parallel to the Base AF, are divided into Two equally by the Plane CD; for the Triangle which will be made on each side of the Plane CD, have their common Base equal to CG; and their sides equal, seeing they are those of a parallelogram. Now it is evident that the Parallelepipedon AB, containeth nothing else but its parallelo∣gram Surfaces, each of which is divided into Two equal Triangles: therefore the parallelepipedon AB, is divided into Two equally by the Plane CD.
The Twenty Seventh and Twenty Eighth Propopositions are useless, according to this way of Demonstration.