Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite v
... Ratios , contains a copious selection of propositions , not only beautiful in themselves , but which pave the way to the higher branches of Geometry , or lead immediately to valuable practical results . The Appendix , without claiming ...
... Ratios , contains a copious selection of propositions , not only beautiful in themselves , but which pave the way to the higher branches of Geometry , or lead immediately to valuable practical results . The Appendix , without claiming ...
Seite 128
... ratio of equality ; if the first of these be greater than the second , it is a ratio of majority ; 128 ELEMENTS OF GEOMETRY . DEFINITIONS. ...
... ratio of equality ; if the first of these be greater than the second , it is a ratio of majority ; 128 ELEMENTS OF GEOMETRY . DEFINITIONS. ...
Seite 129
... ratio is direct , if it follows the order of the terms compared ; it is inverse or reciprocal , when it holds a re- versed order . Thus , if the ratio of A to B be direct , that of B to A is the inverse or reciprocal ratio . 16 ...
... ratio is direct , if it follows the order of the terms compared ; it is inverse or reciprocal , when it holds a re- versed order . Thus , if the ratio of A to B be direct , that of B to A is the inverse or reciprocal ratio . 16 ...
Seite 130
... ratio which one quantity has to another may be considered as compounded of all the connecting ratios among any interposed quantities . Thus , the ratio of A to D is viewed as compounded of that of A to B , that of B to C , and that of C ...
... ratio which one quantity has to another may be considered as compounded of all the connecting ratios among any interposed quantities . Thus , the ratio of A to D is viewed as compounded of that of A to B , that of B to C , and that of C ...
Seite 132
... Ratios and analogies are expressed , by inserting points in pairs between the terms . Thus A : B denotes the ra- tio of A to B ; and the compound symbols A : B :: C : D , signify that the ratio of A to B is the same as that of C to D ...
... Ratios and analogies are expressed , by inserting points in pairs between the terms . Thus A : B denotes the ra- tio of A to B ; and the compound symbols A : B :: C : D , signify that the ratio of A to B is the same as that of C to D ...
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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.