Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite 33
... ABCD be equal , they are also parallel . For draw the diagonal AC . And because AB is equal to DC , BC to AD , and AC is com- mon ; the two triangles ABC and ADC are ( I. 2. ) equal . Conse- quently the angle ACD is equal D to CAB , and ...
... ABCD be equal , they are also parallel . For draw the diagonal AC . And because AB is equal to DC , BC to AD , and AC is com- mon ; the two triangles ABC and ADC are ( I. 2. ) equal . Conse- quently the angle ACD is equal D to CAB , and ...
Seite 39
... ABCD , let the angle at B be equal to the opposite one at D , and the angle at A equal to that at C ; the sides AB and BC are equal and parallel to DC and DA . For all the angles of the figure being equal to four right angles ( I. 31 ...
... ABCD , let the angle at B be equal to the opposite one at D , and the angle at A equal to that at C ; the sides AB and BC are equal and parallel to DC and DA . For all the angles of the figure being equal to four right angles ( I. 31 ...
Seite 41
... ABCD is the square required . B For , by this construction , the figure has all its sides e- qual , and one of its angles ABC a right angle ; which com- prehends the whole of the definition of a square . PROP . XXXVI . PROB . To divide ...
... ABCD is the square required . B For , by this construction , the figure has all its sides e- qual , and one of its angles ABC a right angle ; which com- prehends the whole of the definition of a square . PROP . XXXVI . PROB . To divide ...
Seite 51
... ABCD is equivalent to the rectangle con- tained by its altitude and half the sum of the parallel sides BC and AD . For draw CE parallel to AB ( I. 23. ) , bisect ED ( I. 7. ) in F , and draw FG parallel to AB , meeting the production of ...
... ABCD is equivalent to the rectangle con- tained by its altitude and half the sum of the parallel sides BC and AD . For draw CE parallel to AB ( I. 23. ) , bisect ED ( I. 7. ) in F , and draw FG parallel to AB , meeting the production of ...
Seite 69
... ABCD be a rhomboid : The squares of all the sides AB , BC , CD , and AD , are together equivalent to the squares of the diagonals AC , BD . B For the angles BCE and CBE are equal to the alternate angles DAE and ADE , and the interjacent ...
... ABCD be a rhomboid : The squares of all the sides AB , BC , CD , and AD , are together equivalent to the squares of the diagonals AC , BD . B For the angles BCE and CBE are equal to the alternate angles DAE and ADE , and the interjacent ...
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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.