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 7
... circle BCD ; ( post . 3. ) from the center B , at the distance BA , describe the circle ACE ; and from C , one of the points in which the circles cut one another , draw the straight lines CA , CB to the points A , B. ( post . 1. ) Then ...
... circle BCD ; ( post . 3. ) from the center B , at the distance BA , describe the circle ACE ; and from C , one of the points in which the circles cut one another , draw the straight lines CA , CB to the points A , B. ( post . 1. ) Then ...
Σελίδα 8
... circle CGH , therefore BC is equal to BG ; ( def . 15. ) and because D is the center of the circle GKL , therefore DL is equal to DG , and DA , DB parts of them are equal ; ( 1. 1. ) therefore the remainder ÂL is equal to the remainder ...
... circle CGH , therefore BC is equal to BG ; ( def . 15. ) and because D is the center of the circle GKL , therefore DL is equal to DG , and DA , DB parts of them are equal ; ( 1. 1. ) therefore the remainder ÂL is equal to the remainder ...
Σελίδα 21
... circle DKL ; ( post 3. ) from the center G , at the distance GH , describe the circle HLK ; from K where the circles cut each other draw KF , KG to the points F , G ; Then the triangle KFG shall have its sides equal to the three ...
... circle DKL ; ( post 3. ) from the center G , at the distance GH , describe the circle HLK ; from K where the circles cut each other draw KF , KG to the points F , G ; Then the triangle KFG shall have its sides equal to the three ...
Σελίδα 51
... circle are discussed in these books beyond the definition and the third postulate . When two circles are described ... circle CGH with center B and radius BC , and producing DB the side of the equilateral triangle DBA to meet the ...
... circle are discussed in these books beyond the definition and the third postulate . When two circles are described ... circle CGH with center B and radius BC , and producing DB the side of the equilateral triangle DBA to meet the ...
Σελίδα 66
... circles which pass through these two points . Hence the intersection F of these two perpendiculars , will be the center of a circle which passes through the three points and is called the intersection of the two loci . Sometimes this ...
... circles which pass through these two points . Hence the intersection F of these two perpendiculars , will be the center of a circle which passes through the three points and is called the intersection of the two loci . Sometimes this ...
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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...