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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 ...

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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.
Link to this Item
http://name.umdl.umich.edu/A38722.0001.001
Cite this Item
"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 June 10, 2024.

Pages

PROPOSITION XXX. THEOREM.

RIght Lines Parallel to one and the same, are also Parallel the one to the other.

Let the Lines AB, FE, be Parallel to the Line CD; I say they are Paral∣lel the one to the other. Let the Line GK cut all three.

Demonstration. Seeing that the Lines AB, CD, are Parallel; the Alternate Angles AHI, HID, shall be equal (by the 29th:) and because the Lines CD, FE, are also Parallel, the Exteriour Angle HID shall be equal to the In∣teriour ILE (by the same.) Therefore the Alternate Angles AHI, ILE,

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shall be equal, and the Line AB, FE, Parallels (by the 28th.)

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