Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite 59
... whence , by For CD B the Proposition , the rectangle AD , DB is equivalent to the excess of the square of AC above that of CD , and consequently the rectangle AD , DB , with the square of CD , is equal to the square of AC . Cor . 2. If ...
... whence , by For CD B the Proposition , the rectangle AD , DB is equivalent to the excess of the square of AC above that of CD , and consequently the rectangle AD , DB , with the square of CD , is equal to the square of AC . Cor . 2. If ...
Seite 60
... whence ( I. 11. ) the side BF is equal to BC . By the same reasoning , it may be shown , that the right angled triangle GEF is likewise isosceles . The square of the hypotenuse EF , which is equivalent to the squares of EG 60 ELEMENTS ...
... whence ( I. 11. ) the side BF is equal to BC . By the same reasoning , it may be shown , that the right angled triangle GEF is likewise isosceles . The square of the hypotenuse EF , which is equivalent to the squares of EG 60 ELEMENTS ...
Seite 62
... whence the rectangle IC , with the square of BE , is equivalent to the squares of DB and BE ; or , omitting the common square of BE , the rectangle IC is equivalent to the square of DB . Take away from both the rectangle BK , and there ...
... whence the rectangle IC , with the square of BE , is equivalent to the squares of DB and BE ; or , omitting the common square of BE , the rectangle IC is equivalent to the square of DB . Take away from both the rectangle BK , and there ...
Seite 64
... whence the square of AB is equivalent to the square of BD , together with the rectangle AD , DC . 2. But the square of the straight line BD drawn from the vertex to any point in the base produced , is greater 1 than the square of AB by ...
... whence the square of AB is equivalent to the square of BD , together with the rectangle AD , DC . 2. But the square of the straight line BD drawn from the vertex to any point in the base produced , is greater 1 than the square of AB by ...
Seite 69
... whence twice the squares of AB , BC , or the squares of all the sides of the rhomboid , are equivalent to four times the square of AE and four times the square of BE , that is , to the squares of AC and BD . 3 ELEMENTS OF GEOMETRY ...
... whence twice the squares of AB , BC , or the squares of all the sides of the rhomboid , are equivalent to four times the square of AE and four times the square of BE , that is , to the squares of AC and BD . 3 ELEMENTS OF GEOMETRY ...
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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 sequently side AC 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