Euclid's Elements of geometry, the first four books, by R. Potts. Corrected and improved1864 |
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Side 7
... wherefore AB , BC , CA are equal to one another : and the triangle ABC is therefore equilateral , and it is described upon the given straight line AB . Which was required to be done . PROPOSITION II . PROBLEM . From a given point , to ...
... wherefore AB , BC , CA are equal to one another : and the triangle ABC is therefore equilateral , and it is described upon the given straight line AB . Which was required to be done . PROPOSITION II . PROBLEM . From a given point , to ...
Side 8
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC . ( ax . 1. ) Wherefore from the given point A , a straight line AL ...
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC . ( ax . 1. ) Wherefore from the given point A , a straight line AL ...
Side 9
... wherefore the base BC shall coincide with the base EF ; because the point B coinciding with E , and C with F , if the base BC do not coincide with the base EF , the two straight lines . BC and EF would enclose a space , which is ...
... wherefore the base BC shall coincide with the base EF ; because the point B coinciding with E , and C with F , if the base BC do not coincide with the base EF , the two straight lines . BC and EF would enclose a space , which is ...
Side 10
... wherefore these triangles are equal , ( 1. 4. ) and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG . And , since it ...
... wherefore these triangles are equal , ( 1. 4. ) and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG . And , since it ...
Side 11
... Wherefore , if two angles , & c . Q.E.D. COR . Hence an equiangular triangle is also equilateral . PROPOSITION VII . THEOREM . Upon the same base , and on the same side of it , there cannot be two triangles that have their sides which ...
... Wherefore , if two angles , & c . Q.E.D. COR . Hence an equiangular triangle is also equilateral . PROPOSITION VII . THEOREM . Upon the same base , and on the same side of it , there cannot be two triangles that have their sides which ...
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Euclid's Elements of Geometry, the First Four Books, by R. Potts. Corrected ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ... Euclides Ingen forhåndsvisning tilgjengelig - 1864 |
Vanlige uttrykk og setninger
ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle equal Apply Euc axiom base BC bisecting the angle chord circle ABC circumference construction demonstrated describe a circle diagonals diameter double draw equal angles equal to twice equiangular equilateral triangle Euclid Euclid's Elements exterior angle Geometry given angle given circle given line given point given straight line gnomon greater hypotenuse inscribed intersection isosceles triangle Let ABC line AC line CD line joining lines be drawn meet the circumference opposite angles opposite sides parallel parallelogram pentagon perpendicular porism problem produced Prop proved quadrilateral figure radius rectangle contained remaining angle right angles right-angled triangle segment semicircle shew shewn side BC square on AC tangent THEOREM touches the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
Populære avsnitt
Side 118 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
Side 90 - 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 in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Side 30 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 54 - If two triangles have two sides of the one equal to two sides of the...
Side 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 85 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 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...
Side 41 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Side 126 - EF, that is, AF, is greater than BF : Again, because BE is equal to CE, and FE common to the triangles BEF, CEF, the two sides BE, EF are equal to the two CE, EF; but the angle BEF is greater than the angle CEF ; therefore the base BF is greater (24. 1.) than the base FC ; for the same reason, CF is greater than GF. Again, because GF, FE are greater (20.