Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes .... the first six booksJ. W. Parker & son, 1860 - 361 σελίδες |
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Σελίδα
... shewn the importance of Geometry as one of the most effectual instruments of intellectual education . In page 55 he thus proceeds : - " But besides the value of Mathematical Studies in Education , as a perfect example and complete ...
... shewn the importance of Geometry as one of the most effectual instruments of intellectual education . In page 55 he thus proceeds : - " But besides the value of Mathematical Studies in Education , as a perfect example and complete ...
Σελίδα 8
... shewn that BC is equal to BG , wherefore AL and BC are each of them equal to BG ; and things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC . ( ax . 1. ) Wherefore from the ...
... shewn that BC is equal to BG , wherefore AL and BC are each of them equal to BG ; and things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC . ( ax . 1. ) Wherefore from the ...
Σελίδα 9
... shewn to coincide with the point E ; wherefore the base BC shall coincide with the base EF ; because the point B coinciding with E , and C with F , if the base BC do not coincide with the base EF , the two straight lines BC and EF would ...
... shewn to coincide with the point E ; wherefore the base BC shall coincide with the base EF ; because the point B coinciding with E , and C with F , if the base BC do not coincide with the base EF , the two straight lines BC and EF would ...
Σελίδα 31
... shewn to be equal to BD . Therefore , straight lines which , & c . Q.E.D. PROPOSITION XXXIV . THEOREM . The opposite sides and angles of a parallelogram are equal to one another , and the diameter bisects it , that is , divides it into ...
... shewn to be equal to BD . Therefore , straight lines which , & c . Q.E.D. PROPOSITION XXXIV . THEOREM . The opposite sides and angles of a parallelogram are equal to one another , and the diameter bisects it , that is , divides it into ...
Σελίδα 49
... premiss of a third syllogism , and so on , and thus any process of reasoning is reduced to the strictly syllogistic form . And in this way it is shewn D that the general theorems of Geometry are demonstrated by means NOTES TO BOOK I. 49.
... premiss of a third syllogism , and so on , and thus any process of reasoning is reduced to the strictly syllogistic form . And in this way it is shewn D that the general theorems of Geometry are demonstrated by means NOTES TO BOOK I. 49.
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Συχνά εμφανιζόμενοι όροι και φράσεις
A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC Apply Euc axiom base BC chord circle ABC constr describe a circle diagonals diameter divided double draw equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements exterior angle Geometrical given circle given line given point given straight line given triangle gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line AC lines be drawn meet the circumference multiple opposite angles parallelogram pentagon perpendicular porism problem produced Prop proportionals proved Q.E.D. PROPOSITION quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar similar triangles square on AC tangent THEOREM touch the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 54 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 89 - 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...
Σελίδα 38 - Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.
Σελίδα 144 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 18 - Any two angles of a triangle are together less than two right angles.
Σελίδα 266 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 152 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 7 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line; it is required to draw from the point A a straight line equal to BC.
Σελίδα 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 96 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...