Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson...together with a Selection of Geometrical Exercises from the Senate-house and College Examination Papers .... the first six books, and the portions of the eleventh and twelfth books read at CambridgeLongman, Green, Longman, Roberts, & Green, 1865 - 504 páginas |
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Página 38
... square upon a given straight line . Let AB be the given straight line . C D E. A B. It is required to describe a square upon AB . From the point A draw AC at right angles to AB ; ( 1. 11 ) make AD equal to AB ; ( 1. 3. ) through the ...
... square upon a given straight line . Let AB be the given straight line . C D E. A B. It is required to describe a square upon AB . From the point A draw AC at right angles to AB ; ( 1. 11 ) make AD equal to AB ; ( 1. 3. ) through the ...
Página 40
... square on AD is equal to the square on AB ; to each of these equals add the square on AC ; therefore the squares on AD , AC are equal to the squares on AB , AC : but the squares on AD , AC are equal to the square on DC , ( 1. 47 ...
... square on AD is equal to the square on AB ; to each of these equals add the square on AC ; therefore the squares on AD , AC are equal to the squares on AB , AC : but the squares on AD , AC are equal to the square on DC , ( 1. 47 ...
Página 60
... square being considered as an equilateral rectangle , its area or surface may be expressed numerically if the number of lineal units in a side of the square be given , as is shewn in the note on Prop . I. , Book II . The student will ...
... square being considered as an equilateral rectangle , its area or surface may be expressed numerically if the number of lineal units in a side of the square be given , as is shewn in the note on Prop . I. , Book II . The student will ...
Página 66
... square without including superfluous conditions , and explain the mode of constructing a square upon a given straight line in conformity with such a definition . 96. The sum of the angles of a square is equal to four right angles . Is ...
... square without including superfluous conditions , and explain the mode of constructing a square upon a given straight line in conformity with such a definition . 96. The sum of the angles of a square is equal to four right angles . Is ...
Página 68
... square ADEB , ( 1. 46. ) and through C draw CF parallel to AD or BE , ( I. 31. ) meeting DE in F. Then AE is equal to the rectangles AF , CE . And AE is the square on AB ; and AF is the rectangle contained by BA , AC ; for it is ...
... square ADEB , ( 1. 46. ) and through C draw CF parallel to AD or BE , ( I. 31. ) meeting DE in F. Then AE is equal to the rectangles AF , CE . And AE is the square on AB ; and AF is the rectangle contained by BA , AC ; for it is ...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ... Robert Potts Sin vista previa disponible - 2016 |
Términos y frases comunes
A₁ ABCD AC is equal angle ABC angle ACB angle BAC angle equal Apply Euc base BC bisects the angle chord circle ABC circle described circle whose center circles touch circumscribing circle construction describe a circle diagonals diameter divided draw equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements exterior angle Geometrical given circle given line given point given straight line greater hypotenuse isosceles triangle Let ABC line joining lines be drawn meet the circumference multiple opposite angles parallelogram parallelopiped pentagon perpendicular plane point of contact polygon produced Prop proved Q.E.D. PROPOSITION quadrilateral quadrilateral figure radius rectangle contained rectilineal figure right angles right-angled triangle segment semicircle shew shewn similar triangles solid angle square on AC tangent THEOREM touch the circle triangle ABC vertex vertical angle wherefore
Pasajes populares
Página 23 - 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.
Página xiv - The sluggard is wiser in his own conceit than seven men that can render a reason.
Página 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...
Página 29 - 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.
Página 71 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Página 15 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it, the angles CBA, ABD : these shall either be two right angles, or shall together be equal to two right angles. For...
Página 242 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Página 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Página 34 - Equal triangles, upon equal bases in the same straight line, and towards the same parts, are between the same parallels. Let the equal triangles ABC, DEF be upon equal bases BC, EF, in the same straight line BF, and towards the same parts.
Página 28 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.