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 σελίδες |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 5
... parallelogram is a four - sided figure , of which the opposite sides are parallel : and a diameter , or a diagonal is a straight line joining two of its opposite angles . POSTULATES . I. LET it be granted , that a straight line may be ...
... parallelogram is a four - sided figure , of which the opposite sides are parallel : and a diameter , or a diagonal is a straight line joining two of its opposite angles . POSTULATES . I. LET it be granted , that a straight line may be ...
Σελίδα 30
... parallelogram are equal to one another , and the diameter bisects it , that is , divides it into two equal parts . Let ACDB be a parallelogram , of which BC is a diameter . Then the opposite sides and angles of the figure shall be equal ...
... parallelogram are equal to one another , and the diameter bisects it , that is , divides it into two equal parts . Let ACDB be a parallelogram , of which BC is a diameter . Then the opposite sides and angles of the figure shall be equal ...
Σελίδα 31
... parallelograms ABCD , EBCF be upon the same base BC , and between the same parallels AF , BC . Then the parallelogram ABCD shall be equal to the parallelogram EB CF. AE DF A F A DE F B C B C B C If the sides AD , DF of the parallelograms ...
... parallelograms ABCD , EBCF be upon the same base BC , and between the same parallels AF , BC . Then the parallelogram ABCD shall be equal to the parallelogram EB CF. AE DF A F A DE F B C B C B C If the sides AD , DF of the parallelograms ...
Σελίδα 32
... parallelogram EFGH is equal to the parallelogram EBCH ; therefore the parallelogram ABCD is equal to the parallelogram EFGH . ( ax . 1. ) Therefore , parallelograms upon equal , & c . Q.E.D. 1 PROPOSITION XXXVII . THEOREM . Triangles ...
... parallelogram EFGH is equal to the parallelogram EBCH ; therefore the parallelogram ABCD is equal to the parallelogram EFGH . ( ax . 1. ) Therefore , parallelograms upon equal , & c . Q.E.D. 1 PROPOSITION XXXVII . THEOREM . Triangles ...
Σελίδα 33
... parallelogram GBCA ; ( 1. 34. ) also , because the diameter DF bisects the parallelogram DEFH , therefore the triangle DEF is the half of the parallelogram DEFH ; but the halves of equal things are equal ; ( ax . 7. ) therefore the ...
... parallelogram GBCA ; ( 1. 34. ) also , because the diameter DF bisects the parallelogram DEFH , therefore the triangle DEF is the half of the parallelogram DEFH ; but the halves of equal things are equal ; ( ax . 7. ) therefore the ...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ... Robert Potts Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A₁ ABCD angle ACB angle BAC angle equal Apply Euc base BC bisects the angle chord circle cutting circle described circle whose center circles touch circumscribing circle construction describe a circle diagonals diameter divided draw equal angles equiangular equilateral triangle equimultiples Euclid exterior angle Geometrical given angle given circle given line given point given straight line given triangle greater hypotenuse inscribed circle isosceles triangle Let ABC line joining lines be drawn locus magnitudes meet the circumference opposite sides parallel to BC parallelogram parallelopiped pentagon perpendicular plane point of contact polygon Prop PROPOSITION proved quadrilateral figure radius rectangle contained right angles right-angled triangle segment semicircle shew shewn side BC similar triangles solid angle square on AC tangent THEOREM touch the circle trapezium triangle ABC vertex vertical angle Whence wherefore
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα xiv - The sluggard is wiser in his own conceit than seven men that can render a reason.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.