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 sider |
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Side 10
... demonstrated . PROPOSITION V. THEOR . - The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles ...
... demonstrated . PROPOSITION V. THEOR . - The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles ...
Side 12
... demonstrated to be greater than it ; which is impossible . C E F But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ...
... demonstrated to be greater than it ; which is impossible . C E F But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ...
Side 14
... demonstrated , that two straight lines cannot have a common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B draw BE at right angles to AB ; and because ABC ...
... demonstrated , that two straight lines cannot have a common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B draw BE at right angles to AB ; and because ABC ...
Side 16
... demonstrated to be equal to the same three angles ; and things that are equal to the same are equal ¶ to one another ; therefore the angles CBE , EBD are equal to the angles DBA , ABC ; but CBE , EBD are two right angles ; therefore DBA ...
... demonstrated to be equal to the same three angles ; and things that are equal to the same are equal ¶ to one another ; therefore the angles CBE , EBD are equal to the angles DBA , ABC ; but CBE , EBD are two right angles ; therefore DBA ...
Side 17
... demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. PROPOSITION XV . THEOR . - If two straight lines cut one ...
... demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. PROPOSITION XV . THEOR . - If two straight lines cut one ...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ... Euclid Uten tilgangsbegrensning - 1845 |
Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ... Euclid Uten tilgangsbegrensning - 1845 |
Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ... Euclid Uten tilgangsbegrensning - 1845 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 12 - If two triangles have two sides of the one equal to two sides of the...
Side 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.
Side 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.
Side 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.
Side 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.
Side 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
Side 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.
Side 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.
Side 66 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Side 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.