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 9
... triangle ABC to the triangle DEF ; and the other angles to which the equal sides are opposite shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . D B C E F For , if the triangle ...
... triangle ABC to the triangle DEF ; and the other angles to which the equal sides are opposite shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . D B C E F For , if the triangle ...
Seite 10
... triangle ABC ; and it has also been proved , that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . Therefore the angles at the base , & c . Q.E.D. COR . Hence an equilateral triangle is ...
... triangle ABC ; and it has also been proved , that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . Therefore the angles at the base , & c . Q.E.D. COR . Hence an equilateral triangle is ...
Seite 11
... ABC , because DB is equal to AC , and BC is common to both triangles , the two sides DB , BC are equal to the two ... triangle DBC is equal to the triangle ABC , the less equal to the greater , which is absurd . ( ax . 9. ) Therefore AB ...
... ABC , because DB is equal to AC , and BC is common to both triangles , the two sides DB , BC are equal to the two ... triangle DBC is equal to the triangle ABC , the less equal to the greater , which is absurd . ( ax . 9. ) Therefore AB ...
Seite 12
... triangle ACD , therefore the angles ECD , FDC upon the other side of the ... ABC , DEF be two triangles , having the two sides AB , AC , equal to the two ... triangle ABC be applied to DEF , so that the point B be on E , and the straight ...
... triangle ACD , therefore the angles ECD , FDC upon the other side of the ... ABC , DEF be two triangles , having the two sides AB , AC , equal to the two ... triangle ABC be applied to DEF , so that the point B be on E , and the straight ...
Seite 13
... triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to each ; and the base DF is ... triangle ABC ; ( 1. 1. ) A D B and bisect the angle ACB by the straight line CD meeting AB in the point D. ( I. 9 ...
... triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to each ; and the base DF is ... triangle ABC ; ( 1. 1. ) A D B and bisect the angle ACB by the straight line CD meeting AB in the point D. ( I. 9 ...
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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...