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" 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
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A Course of Mathematics: For the Use of Academies as Well as ..., Volume 1

Charles Hutton - Mathematics - 1812
...angles, and there remain all the outward angles equal to four right angles (by ax. 3). 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 Perpendicular,...
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volume 2

Charles Butler - Mathematics - 1814 - 528 pages
...may be shewn of every point in CT, •.• CT is without the circle. QED Cor. Hence it appears that the shortest line that can be drawn from a given point to a given straight line, is that which is perpendicular to the latter. 185. In the enunciation of this proposition...
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A Course of Mathematics: For the Use of Academies, as Well as Private Tuition

Charles Hutton - Mathematics - 1818 - 646 pages
...there remain all the outward angles equal to four right angles (by ax. 3). THEOREM XXl. A PERPEND1CULAR is the Shortest Line that can be drawn from a Given Point to an 1ndefinite Line. And, of any other Lines drawn from the same Point, those that are Nearest he Perpendicular,...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 618 pages
...remain all the outward angles equal to four right angles (by ax. 3). THEOREM XXI. A PERPENDICULAR in the Shortest Line that can be drawn from a Given Point to an Indefinite Line. And, of any other Linct drawn from the same Point, those that are Nearest the Perpendicular,...
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A Course of Mathematics for the Use of Academies: As Well as ..., Volume 1

Charles Hutton - Mathematics - 1825
...angles, and there remain all the outward angles equal to four right angles (by as. 3). THEOREM XXI. A PERPENDICULAR is the Shortest Line that can be drawn from a Oiven Point to an Indefinite Line. And, of any other Linen drawn from the same Point, those thai are...
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Self-examinations in Euclid

John Martin Frederick Wright - Euclid's Elements - 1829 - 206 pages
...drawn from one point to another is the straight line, The above is the method of Legendre. 123. What is the shortest line that can be drawn from a given point to a given \ ? Let A be the given point. BC the given | . From A let fall a J_ AD upon BC, take -t: G^ ^E i> any...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...beyond the vertex, the exterior angle is double of either of the angles at the base. 4. Of all lines that can be drawn from a given point to a given line, the perpendicular upon it is the least ; and of all others, that which is nearest to the perpendicular...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1837 - 332 pages
...side BC. And because the side DA is equal to AB, and AC *^ 42 ADDITIONAL PROPOSITIONS. PROP. A. THEOR. A perpendicular is the shortest line that can be drawn from a point, situated without a straight line, to that line: any two oblique lines drawn from the same point...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...DAC is a right angle ; therefore also BAC is a right angle. ADDITIONAL PROPOSITIONS. PROP. A. THEOR. A perpendicular is the shortest line that can be drawn from a point, situated without a straight line, to that line : any two oblique lines drawn from the same point...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...equal : prove that the line joining the given points Will bisect the given line at right angles. 4. The perpendicular is the shortest line that can be drawn from a given point to a given line, and that which is nearer to the perpendicular is less than one more remote ; and from the same given...
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