Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes .... the first six booksJ. W. Parker & son, 1860 - 361 Seiten |
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Seite 3
... circumference , and is such that all straight lines drawn from a certain point within the figure to the circumference , are equal to one another . XVI . And this point is called the center of the circle . XVII . A diameter of a circle ...
... circumference , and is such that all straight lines drawn from a certain point within the figure to the circumference , are equal to one another . XVI . And this point is called the center of the circle . XVII . A diameter of a circle ...
Seite 49
... circumference are equal . In a similar way may be supplied the reserved premiss in every enthy- meme . The conclusion of two enthymemes may form the major and minor premiss of a third syllogism , and so on , and thus any process of ...
... circumference are equal . In a similar way may be supplied the reserved premiss in every enthy- meme . The conclusion of two enthymemes may form the major and minor premiss of a third syllogism , and so on , and thus any process of ...
Seite 51
... circumference in G : next , with center D and radius DG , describing the circle GKL , and then producing DA to meet the circumference in L. By a similar construction the less of two given straight lines may be produced , so that the ...
... circumference in G : next , with center D and radius DG , describing the circle GKL , and then producing DA to meet the circumference in L. By a similar construction the less of two given straight lines may be produced , so that the ...
Seite 98
... circumference in H. The square described upon EH shall be equal to the given recti- lineal figure A. Join GH . Then because the straight line BF is divided into two equal parts in the point G , and into two unequal parts in the point E ...
... circumference in H. The square described upon EH shall be equal to the given recti- lineal figure A. Join GH . Then because the straight line BF is divided into two equal parts in the point G , and into two unequal parts in the point E ...
Seite 120
... be further from the center . VI . A segment of a circle is the figure contained by a straight line , and the arc or the part of the circumference which it cuts off . VII . The angle of a segment is that which BOOK III .
... be further from the center . VI . A segment of a circle is the figure contained by a straight line , and the arc or the part of the circumference which it cuts off . VII . The angle of a segment is that which BOOK III .
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 54 - If two triangles have two sides of the one equal to two sides of the...
Seite 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...
Seite 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.
Seite 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.
Seite 18 - Any two angles of a triangle are together less than two right angles.
Seite 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.
Seite 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.
Seite 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.
Seite 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Seite 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...