Elements of Geometry Containing the First Six Books of Euclid With a Supplemen
Elements of Geometry Containing the First Six Books of Euclid With a Supplemen
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y ELEMENTS OF GEOMETRY.
SUPPLEMENT.
BOOK FIKST. OP THE QUADEATURE OF THE CIRCLE.
DEFINITIONS.
I. A cliord of an arc of a circle is the straight line joining the ei- remities of the arc ; or the straight line which subtends the arc.
II. The perimeter of any figure is the length of the line, or lines, by which it is bounded.
AXIOM I.
The least line that can be drawn between two points is a straight line ; and if two figures have the same straight line for their base, that which is contained withi...n the other, if its bounding line or lines be not anywhere convex towards the base, has the less perimeter.
Cor. 1. Hence the perimeter of any polygon inscribed in a circle is less tlian the circumference of the circle.
Cor. 2. If from a point two straight lines be drawn touching a circle, these two lines are together greater than the arc inter- cepted between them ; and hence the perimeter of any polygon described about a circle is greater than the circumference of the circle, AXIOM II.
The space which is greater than any polygon that can be inscribed in a given circle, and less than any polygon that can be described about it, is equal to the circle.
What to read after Elements of Geometry Containing the First Six Books of Euclid With a Supplemen?
You can find similar books in the "Read Also" column, or choose other free books by John Playfair to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
y ELEMENTS OF GEOMETRY.
SUPPLEMENT.
BOOK FIKST. OP THE QUADEATURE OF THE CIRCLE.
DEFINITIONS.
I. A cliord of an arc of a circle is the straight line joining the ei- remities of the arc ; or the straight line which subtends the arc.
II. The perimeter of any figure is the length of the line, or lines, by which it is bounded.
AXIOM I.
The least line that can be drawn between two points is a straight line ; and if two figures have the same straight line for their base, that which is contained withi...n the other, if its bounding line or lines be not anywhere convex towards the base, has the less perimeter.
Cor. 1. Hence the perimeter of any polygon inscribed in a circle is less tlian the circumference of the circle.
Cor. 2. If from a point two straight lines be drawn touching a circle, these two lines are together greater than the arc inter- cepted between them ; and hence the perimeter of any polygon described about a circle is greater than the circumference of the circle, AXIOM II.
The space which is greater than any polygon that can be inscribed in a given circle, and less than any polygon that can be described about it, is equal to the circle.
What to read after Elements of Geometry Containing the First Six Books of Euclid With a Supplemen?
You can find similar books in the "Read Also" column, or choose other free books by John Playfair to read onlineMoreLess
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