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.
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 V. THEOREM.
IF a Line be Perpendicular to three other Lines which cut one the other in the same Point, these three Lines shall be in the same Plane.
If the Line AB be perpendicular to three Lines BC, BD, BE, which cut one another in the point B, the Lines BC, BD, BE, are in the same plane. Let the plane AE be the Plane of the Lines AB, BE; and let CF be the Plane of the Lines BC, BD. If BE was the common section of the Two Planes, BE would be in the Plane of the Lines BC, BD, as we pretend it should. Now if BE be not the common section; let it be BG.
descriptionPage 316
Demonstration. AB is perpendicular to the Lines BC, BD; it is then perpendi∣cular to the Plane CF, (by the 4th. and 5th. Def.) AB shall be also perpendicular to BG. Now it is supposed that it is perpendicular to BE; thence the Angles ABE, ABG, would be right, and equal, and notwithstanding the one is a part of the other. So then the Two Planes cannot have any other common section besides BE; it is therefore in the Plane CF.
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