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 8
... equal to DG , and DA , DB parts of them are equal ; ( 1. 1. ) therefore the remainder AL is equal to the remainder BG ; ( ax . 3. ) but it has been shewn that BC is equal to BG , wherefore AL and BC are each of them equal to BG ; and ...
... equal to DG , and DA , DB parts of them are equal ; ( 1. 1. ) therefore the remainder AL is equal to the remainder BG ; ( ax . 3. ) but it has been shewn that BC is equal to BG , wherefore AL and BC are each of them equal to BG ; and ...
Página 9
... equal to the angle EDF ; therefore also the point C shall coincide with the point F , because AC is equal to DF ; but the point B was shewn to coincide with the point E ; wherefore the base BC shall coincide with the base EF ; because ...
... equal to the angle EDF ; therefore also the point C shall coincide with the point F , because AC is equal to DF ; but the point B was shewn to coincide with the point E ; wherefore the base BC shall coincide with the base EF ; because ...
Página 10
... equal to the triangle AGB , also the remaining angles of the one are equal to the remaining angles of the other , each to each , to which the equal sides are opposite ; viz . the angle ACF to the angle ABG , and the angle AFC to the ...
... equal to the triangle AGB , also the remaining angles of the one are equal to the remaining angles of the other , each to each , to which the equal sides are opposite ; viz . the angle ACF to the angle ABG , and the angle AFC to the ...
Página 16
... equal to the three angles DBE , EBA , ABC . But the angles CBE , EBD have been proved equal to the same three angles ; and things which are equal to the same thing , are equal to one another ; therefore the angles CBE , EBD are equal to ...
... equal to the three angles DBE , EBA , ABC . But the angles CBE , EBD have been proved equal to the same three angles ; and things which are equal to the same thing , are equal to one another ; therefore the angles CBE , EBD are equal to ...
Página 21
... equal to A , B , C , each to each . Α K B D F G E C Take a straight line DE terminated at the point D , but unlimited towards E , make DF equal to A , FG equal to B , and GH equal to C ; ( 1. 3. ) from the center F , at the distance FD ...
... equal to A , B , C , each to each . Α K B D F G E C Take a straight line DE terminated at the point D , but unlimited towards E , make DF equal to A , FG equal to B , and GH equal to C ; ( 1. 3. ) from the center F , at the distance FD ...
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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.