Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 páginas |
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Página 13
... triangles are equal , which have all the sides of the one equal to those of the other . Let the two triangles ABC and DFE have the side AB equal to DF , AC to DE , and BC to FE : These triangles are equal . For conceive the triangle ACB ...
... triangles are equal , which have all the sides of the one equal to those of the other . Let the two triangles ABC and DFE have the side AB equal to DF , AC to DE , and BC to FE : These triangles are equal . For conceive the triangle ACB ...
Página 14
... ABC contained by the former equal to DEF which is contained by the latter : These triangles are equal . For let the triangle ABC be applied to DEF : The ver- tex B being placed on E , and the side BA on ED , the ex- tremity A must fall ...
... ABC contained by the former equal to DEF which is contained by the latter : These triangles are equal . For let the triangle ABC be applied to DEF : The ver- tex B being placed on E , and the side BA on ED , the ex- tremity A must fall ...
Página 15
... triangles will be thus formed , all of them equal to the original triangle C ABC . Consequently the angle ABD is double of ABC , ABE triple , ABF quadruple , ABG quintuple , & c . 1 H If the sides AB and BC of the given BOOK I. 15.
... triangles will be thus formed , all of them equal to the original triangle C ABC . Consequently the angle ABD is double of ABC , ABE triple , ABF quadruple , ABG quintuple , & c . 1 H If the sides AB and BC of the given BOOK I. 15.
Página 16
... triangle DFE , and draw the straight line BF : The angle ABC is bisected by BF . For the two triangles DBF and EBF ... ABC , which the opposite seg- ments BA and BC make with each other , being equal to two right angles , the straight ...
... triangle DFE , and draw the straight line BF : The angle ABC is bisected by BF . For the two triangles DBF and EBF ... ABC , which the opposite seg- ments BA and BC make with each other , being equal to two right angles , the straight ...
Página 18
... triangles ( I. 1. ) ACB and ADB , and join their vertices C and D by a straight line cutting AB in the point E : AB is bisected in E. For the sides AC and AD of the triangle ... ABC , is greater than either of the op- posite and interior ...
... triangles ( I. 1. ) ACB and ADB , and join their vertices C and D by a straight line cutting AB in the point E : AB is bisected in E. For the sides AC and AD of the triangle ... ABC , is greater than either of the op- posite and interior ...
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Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... University Professor Emeritus John Leslie, Sir Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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
Página 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
Página 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.
Página 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. .
Página 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
Página 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,
Página 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
Página 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.
Página 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.