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" A perpendicular is the shortest line that can be drawn from a given point to a given line. "
A Course of Mathematics: In Two Volumes : for the Use of Academies, as Well ... - Page 290
by Charles Hutton - 1816
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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...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 616 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, are less than those More...
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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^...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 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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Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 248 pages
...double the number of sides and subtract 4, the right angle being the unit of measure.! THEOREM XVII. A perpendicular is the shortest line that can be drawn...other lines drawn from the same point, those that are equally distant from the perpendicular are equal, and those nearest the perpendicular are less than...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 326 pages
...sum of the angles CBF and FBD, that is, to the whole angle CBD (Ax. II), PROPOSITION XXVI. THEOREM. A perpendicular is the shortest line that can be drawn from a given point to a line of indefinite length ; and of any other lines drawn from the same point, those that are nearest...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 218 pages
...exceed two right angles : hence, at least two angles of every triangle must be acute. THEOREM XVIII. I. A perpendicular is the shortest line that can be drawn from a given point to a given line. II. If any number of lines be drawn from the same point, those which are nearest the...
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