Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes; a Series of Questions on Each Book; and a Selection of Geometrical Exercises from the Senate-house and College Examination Papers, with Hints, &c. Designed for the Use of the Junior Classes in Public and Private Schools. the first six books, and the portions of the eleventh and twelfth books read at Cambridge |
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Seite 9
Then shall the base BC be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles to which the equal sides are opposite shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ...
Then shall the base BC be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles to which the equal sides are opposite shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ...
Seite 10
and the triangle AFC is equal to the triangle ÀGB , also the remaining angles of the one are equal to the remaining ... to which the equal sides are opposite ; viz . the angle ACF to the angle ABG , and the angle AFC to the angle AGB .
and the triangle AFC is equal to the triangle ÀGB , also the remaining angles of the one are equal to the remaining ... to which the equal sides are opposite ; viz . the angle ACF to the angle ABG , and the angle AFC to the angle AGB .
Seite 13
To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle . is required to bisect it . A D E F B с In AB take any point D ; from A C cut off AE equal to AD , ( 1. 3. ) ...
To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle . is required to bisect it . A D E F B с In AB take any point D ; from A C cut off AE equal to AD , ( 1. 3. ) ...
Seite 14
Then CF drawn from the point C , shall be at right angles to AB . Because DC is equal to EC , and FC is common to the two triangles DCF , ECF ; the two sides DC , CF are equal to the two sides EC , CF , each to each ; and the base DF is ...
Then CF drawn from the point C , shall be at right angles to AB . Because DC is equal to EC , and FC is common to the two triangles DCF , ECF ; the two sides DC , CF are equal to the two sides EC , CF , each to each ; and the base DF is ...
Seite 15
therefore the angle FHC is equal to the angle GHC ; ( 1. 8. ) and these are adjacent angles . But when a straight line standing on another straight line , makes the adjacent angles equal to one another , each of them is a right angle ...
therefore the angle FHC is equal to the angle GHC ; ( 1. 8. ) and these are adjacent angles . But when a straight line standing on another straight line , makes the adjacent angles equal to one another , each of them is a right angle ...
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ABCD Algebraically Apply base bisected Book chord circle circumference common construction contained definition demonstrated described diagonals diameter difference distance divided double draw drawn equal equal angles equiangular equilateral triangle equimultiples Euclid extremities fall figure formed four fourth Geometrical given circle given line given point given straight line greater half Hence inscribed intersection join less Let ABC line drawn magnitudes manner mean meet multiple opposite sides parallel parallelogram pass perpendicular plane problem produced Prop proportionals proved Q.E.D. PROPOSITION radius ratio reason rectangle rectangle contained regular remaining respectively right angles segment semicircle shew shewn sides similar solid square straight line taken tangent THEOREM third touch triangle ABC twice units vertex wherefore whole
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Seite 6 - 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 118 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
Seite 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Seite 317 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Seite 90 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Seite 88 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Seite 30 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 9 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Seite 22 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other...
Seite 92 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts...
Bibliografische Informationen
| Titel | Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes; a Series of Questions on Each Book; and a Selection of Geometrical Exercises from the Senate-house and College Examination Papers, with Hints, &c. Designed for the Use of the Junior Classes in Public and ... School edition |
| Autor/in | Robert Potts |
| Verlag | Longman, Green, Longman, Roberts, and Green, 1868 |
| Original von | University of Michigan |
| Digitalisiert | 9. Juni 2007 |
| Länge | 410 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |