712357
[Translation: ]
[Commentary:
This is the first of a set of 11 pages containing propositions from Book I of Conics of Apollonius. The edition used by Harriot was Commandino's Apollonii Pergaei conicorum libri quattuor
(Apollonius , but Harriot translated the verbal propositions and proofs into his own symbolic notation.
English translations of the propositions are taken from Dana Densmore Apollonius of Perga: Conics Books I–III, Green Lion Press, 1998.
Proposition 11 of Book I is Apollonius's definition of a
I.11 If a cone is cut by a plane through its axis, and also cut by another plane cutting the base of the cone in a straight line perpendicular to the base of the axial triangle, and if, further, the diameter of the section is parallel to one side of the axial triangle, and if any straight line is drawn from the section of the cone to its diameter such that this straight line is parallel to the common section of the cutting plane and of the cone's base, then this straight line to the diameter will equal in square the rectangle contained by the straight line from the section's vertex to where the straight line to the diameter cuts it off, and another straight line which has the same ratio to the straight line between the angle of the cone and the vertex of the section as the square on the base of the axial triangle has to the rectangle contained by the remaining two sides of the triangle. And let such a section be called a parabola.]
English translations of the propositions are taken from Dana Densmore Apollonius of Perga: Conics Books I–III, Green Lion Press, 1998.
Proposition 11 of Book I is Apollonius's definition of a
I.11 If a cone is cut by a plane through its axis, and also cut by another plane cutting the base of the cone in a straight line perpendicular to the base of the axial triangle, and if, further, the diameter of the section is parallel to one side of the axial triangle, and if any straight line is drawn from the section of the cone to its diameter such that this straight line is parallel to the common section of the cutting plane and of the cone's base, then this straight line to the diameter will equal in square the rectangle contained by the straight line from the section's vertex to where the straight line to the diameter cuts it off, and another straight line which has the same ratio to the straight line between the angle of the cone and the vertex of the section as the square on the base of the axial triangle has to the rectangle contained by the remaining two sides of the triangle. And let such a section be called a parabola.]
Appol. lib. 1. prop. 11. De
[Translation: Apollonius, Book I, Proposition 11. On ]
[Translation: Apollonius, Book I, Proposition 11. On ]
Aliter demonstrationem
ordinavimus ut
[Translation: Another demonstration, which we have ordered as ]
ordinavimus ut
[Translation: Another demonstration, which we have ordered as ]
Ratio componitur
[Translation: Ratio composed ]
[Translation: Ratio composed ]
[Translation: ]
zoom in
zoom out
zoom area
full page
page width
set mark
remove mark
get reference
digilib