Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite 43
... hypotenuse ; either of the sides which contain it , the base ; and the other side , the perpen- dicular . 2. The altitude of a triangle is a perpendicular let fall from the vertex upon the base or its ex- tension . 3. The altitude of a ...
... hypotenuse ; either of the sides which contain it , the base ; and the other side , the perpen- dicular . 2. The altitude of a triangle is a perpendicular let fall from the vertex upon the base or its ex- tension . 3. The altitude of a ...
Seite 52
... hypotenuse of a right - angled triangle , is equivalent to the squares of the two sides . Let the triangle ABC be right - angled at B ; the square described on the hypotenuse AC is equivalent to BF and BI the squares of the sides AB and ...
... hypotenuse of a right - angled triangle , is equivalent to the squares of the two sides . Let the triangle ABC be right - angled at B ; the square described on the hypotenuse AC is equivalent to BF and BI the squares of the sides AB and ...
Seite 53
... hypotenuse , contains the same space as both together of the squares described on the two sides AB and BC . Cor . Hence the square of a side AB is equivalent to the rectangle under the hypotenuse AC and the adjacent seg- ment AN made by ...
... hypotenuse , contains the same space as both together of the squares described on the two sides AB and BC . Cor . Hence the square of a side AB is equivalent to the rectangle under the hypotenuse AC and the adjacent seg- ment AN made by ...
Seite 54
... hypotenuse of a right - angled triangle - a proper- ty which readily suggests another method of erecting a per- pendicular at the extremity of a straight line . PROP . XII . PROB . To find the side of a square equivalent to any number ...
... hypotenuse of a right - angled triangle - a proper- ty which readily suggests another method of erecting a per- pendicular at the extremity of a straight line . PROP . XII . PROB . To find the side of a square equivalent to any number ...
Seite 55
... hypotenuse CF is equivalent to B E F the squares of CD and DF ( II . 10. ) , and consequently ta- king the square of CD from both , the excess of the square of CF above that of CD is equivalent to the square of DF , or the square of DF ...
... hypotenuse CF is equivalent to B E F the squares of CD and DF ( II . 10. ) , and consequently ta- king the square of CD from both , the excess of the square of CF above that of CD is equivalent to the square of DF , or the square of DF ...
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Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... University Professor Emeritus John Leslie, Sir Keine Leseprobe verfügbar - 2016 |
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ABCD adjacent angle altitude angle ABC angle ADB angle BAC base AC bisect centre chord circle circumference consequently construction contained angle cosine decagon denote describe diameter difference distance diverging lines divided draw equal to BC equilateral triangle equivalent to twice evidently exterior angle Geometry given greater half Hence hypotenuse inscribed isosceles triangle join let fall likewise measure parallel perpendicular point G polygon PROB PROP Proposition quadrilateral figure quantities radius ratio rectangle rectangle contained rectilineal figure rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter side AC sides AB sinB sine square of AB square of AC straight line tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore
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Seite 22 - THEOR. Two sides of a triangle are together greater than the third side. The two sides AB and BC of the triangle ABC are together greater than the third side AC. For produce AB until DB be equal to the side BC, and join CD. Because BC is equal to BD, the angle BCD is equal to BDC (I.
Seite 292 - axiom, (If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles, these straight lines, being continually produced, will at length meet on that side on which are the angles which are less
Seite 10 - circumference. 35. The diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference. It is obvious that all radii of the same circle are equal to each other and to a
Seite 50 - PROB. With a given straight line to construct a rhomboid equivalent to a given rectilineal figure, and having an angle equal to a given angle. Let it be required to construct, with the straight line L, a rhomboid, containing a given space, and having an angle equal to K. Construct (II.
Seite 144 - Proposition is named inverse, or perturbate, equality. PROP. XIX. THEOR. If there be any number of proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. .
Seite 236 - &c. &c. PROP. IV. THEOR. The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs to the tangent of half
Seite 110 - Hence a regular twenty-sided figure may be described on a given straight line, by first constructing on it an isosceles triangle having each of the angles at the base double of the vertical angle,
Seite 30 - THEOR. If a straight line fall upon two parallel straight lines, it will make the alternate angles equal, the exterior angle equal to the interior opposite one, and the two interior angles on the same side together equal to two right angles. • Let the straight line EFG fall upon the parallels AB and CD ; the alternate angles AGF and DFG are equal, the
Seite 137 - founded the two following theorems. PROP. VII. THEOR. The terms of an analogy are proportional by inversion, or the second is to the first, as the fourth to the third. Let A : B : : C : D ; then inversely B : A : : D : C.
Seite 88 - THEOR. The angle in a semicircle is a right angle, the angle in a greater segment is acute, and the angle in a smaller segment is obtuse. Let ABD be an angle in a semicircle, or that stands on the semicircumference AED; it is a right angle.