Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books and the First Twenty-one Propositions of the Eleventh Book ...T. Stevenson, 1845 - 199 σελίδες |
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Σελίδα 7
... BC is equal to BA : But it has been proved that CA is equal to AB ; there- fore CA , CB are each of them equal to AB ; But things which are equal to the same are equal to one tion . another ; therefore CA is equal to CB ; wherefore ...
... BC is equal to BA : But it has been proved that CA is equal to AB ; there- fore CA , CB are each of them equal to AB ; But things which are equal to the same are equal to one tion . another ; therefore CA is equal to CB ; wherefore ...
Σελίδα 8
... equal to BC . B G K H D A E Because the point B is the centre of the circle CGH , BC is equal to BG ; * And because D is the centre of the circle GKL , DL is equal to DG , and † DA , DB , parts of them , are equal ; therefore the ...
... equal to BC . B G K H D A E Because the point B is the centre of the circle CGH , BC is equal to BG ; * And because D is the centre of the circle GKL , DL is equal to DG , and † DA , DB , parts of them , are equal ; therefore the ...
Σελίδα 9
... equal to two sides of the other , each to each ; and have likewise the angles contained by those sides equal to one ... BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles to which B ...
... equal to two sides of the other , each to each ; and have likewise the angles contained by those sides equal to one ... BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles to which B ...
Σελίδα 10
... equal , and the triangles be equal , and their other angles to which the equal sides are opposite shall be equal ... BC is common to the two triangles BFC , CGB ; wherefore the triangles are equal † , and their remaining angles ...
... equal , and the triangles be equal , and their other angles to which the equal sides are opposite shall be equal ... BC is common to the two triangles BFC , CGB ; wherefore the triangles are equal † , and their remaining angles ...
Σελίδα 11
... equal to AC , one of them is greater than the other . Let AB be the greater ; and from it cut * off DB equal to AC , the less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , † and BC common to both ...
... equal to AC , one of them is greater than the other . Let AB be the greater ; and from it cut * off DB equal to AC , the less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , † and BC common to both ...
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ABCD adjacent angles angle ABC angle ACB angle BAC angle BCD angle DEF angle EDF angles equal base BC BC is equal bisected centre circle ABC Constr describe diameter double draw equal angles equal to F equiangular equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio join less Let ABC Let the straight likewise meet multiple opposite angle parallel to BC parallelogram perpendicular plane polygon proportionals Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle sides square of AC straight line AB straight line AC THEOR THEOR.-If three straight lines tiple touches the circle triangle ABC triangle DEF twice the rectangle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 12 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 29 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Σελίδα 143 - 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 69 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Σελίδα 20 - If from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let the two straight lines BD.
Σελίδα 102 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater; that is, ' when the less is contained a certain number of times
Σελίδα 44 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 71 - The opposite angles of any quadrilateral figure described in a circle, are toe/ether equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD : any two of its opposite angles are together equal to two right angles.
Σελίδα 66 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Σελίδα 83 - 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.