Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite 73
... semicircle , and the arc ADB is a semicircumference . PROP . II . THEOR . A straight line cuts the circumference of a cir- cle only in two points . If the straight line AB cut the circumference of a circle in D , it can only meet it ...
... semicircle , and the arc ADB is a semicircumference . PROP . II . THEOR . A straight line cuts the circumference of a cir- cle only in two points . If the straight line AB cut the circumference of a circle in D , it can only meet it ...
Seite 88
... 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 . For ABD ...
... 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 . For ABD ...
Seite 89
... semicircle . Schol . From the remarkable property , that the angle in a semicircle is a right angle , may be derived an elegant me- thod of drawing perpendiculars . PROP . XX . THEOR . The perpendicular at the extremity of a diame- ter ...
... semicircle . Schol . From the remarkable property , that the angle in a semicircle is a right angle , may be derived an elegant me- thod of drawing perpendiculars . PROP . XX . THEOR . The perpendicular at the extremity of a diame- ter ...
Seite 90
... , the angle KBA is a- cute , and consequently its adjacent angle D'BA is obtuse . Thus the revolving line DE , when it meets the semicir . cumference AHB , makes an acute angle with the diame- 90 ELEMENTS OF GEOMETRY .
... , the angle KBA is a- cute , and consequently its adjacent angle D'BA is obtuse . Thus the revolving line DE , when it meets the semicir . cumference AHB , makes an acute angle with the diame- 90 ELEMENTS OF GEOMETRY .
Seite 91
... semicircle ; wherefore AEB is a right angle ( III . 19. ) , and the remaining acute an- gles BAE , ABE of the triangle , be- ing together equal to another right angle , are equal to ABE and EBD , which compose the right angle ABD ...
... semicircle ; wherefore AEB is a right angle ( III . 19. ) , and the remaining acute an- gles BAE , ABE of the triangle , be- ing together equal to another right angle , are equal to ABE and EBD , which compose the right angle ABD ...
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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 |
Häufige Begriffe und Wortgruppen
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 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 sine square of AC squares of AB straight line tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore
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Seite 30 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Seite 333 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...
Seite 294 - 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...
Seite 10 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Seite 137 - Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.
Seite 84 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Seite 292 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Seite 93 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Seite 38 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 58 - The rectangle contained by the sum and difference of two straight lines is equivalent to the difference of the squares of these lines.