Books Books
The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line; and...
Elements of Geometry and Trigonometry: With Applications in Mensuration - Page 30
by Charles Davies - 1886 - 324 pages

## Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...angles, and there remain all the exterior angles equal to four right angles (by ax. 3). QED THEOREM XXI. A perpendicular is the shortest line that can be drawn from a given point to an indefinite line. And, of any other lines drawn from the same point, those that are nearest -the...

## The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...that AF is greater than the diagonal of the square. 21. The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line; and of others, that which is nearer to the perpendicular is less than the more remote;...

## Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...opposite the greater angle, AB is less than AC; and AC may be any line not identical with AB ; therefore a perpendicular is the shortest line that can be drawn from A to the line DE. 2d. As the two angles, ACB and ACD, are together equal to two right angles, (Th. 1),...

## Proceedings, Volume 24

Literary and Philosophical Society of Liverpool - 1870 - 308 pages
...I. 15. After I. 11, he neglects to prove the property analogous to that in III. 7 and 8, viz., " the perpendicular is the shortest line that can be drawn from a given point to a given line ; and of the rest, the line which is nearer to the perpendicular is less than one more remote : also...

## Elements of geometry, with ... trigonometry

André Darré - 1872 - 222 pages
...MN ; then, drawing PD, AP and AD are both perpendicular to PD (124), which is absurd (21). Cor. ii. A perpendicular is the shortest line that can be drawn from a given point to a plane ; for AP is less than any line such as AE drawn from the point A to the plane MN (48). Hence,...

## The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter MASON - Geometry - 1872 - 212 pages
...their vertices, when produced, will bisect the base and be at right angles to it. (I. 1-8.) 16. The perpendicular is the shortest line that can be drawn from a given point to a given straight line. (1. 1-19.) 17. Of all the lines that can be drawn from a given point to a given straight...

## The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...that shall be bisected by another given straight line. 11. The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line ; and of others, that which is nearer to the perpendicular is less than the more remote...

## Elements of Plane Geometry, Part 1

Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...right angles, if the angles are all equal each must be a right angle. PROPOSITION XXXI.—THEOREM. A. perpendicular is the shortest line that can be drawn from a given point to a given line; two oblique lines drawn from this point to two points on the line equidistant from the perpendicular...