Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes .... the first six booksJ. W. Parker & son, 1860 - 361 sider |
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Side
... reason for the belief that is in him , and not to leave him in the con- dition of Solomon's sluggard , who is wiser in his own conceit than seven men that can render a reason . " And in his more recent work entitled , " Of a Liberal ...
... reason for the belief that is in him , and not to leave him in the con- dition of Solomon's sluggard , who is wiser in his own conceit than seven men that can render a reason . " And in his more recent work entitled , " Of a Liberal ...
Side 21
... reason , the exterior angle CED of the triangle ABE is greater than the interior and opposite angle BAC ; and it has been demonstrated , that the angle BDC is greater than the angle CEB ; much more therefore is the angle BDC greater ...
... reason , the exterior angle CED of the triangle ABE is greater than the interior and opposite angle BAC ; and it has been demonstrated , that the angle BDC is greater than the angle CEB ; much more therefore is the angle BDC greater ...
Side 32
... reason , EF is equal to BC ; wherefore AD is equal to EF ; ( ax . 1. ) and DE is common ; therefore the whole , or the remainder AE , is equal to the whole , or the remainder DF ; ( ax . 2 or 3. ) and AB is equal to DC ; ( 1. 24 ...
... reason , EF is equal to BC ; wherefore AD is equal to EF ; ( ax . 1. ) and DE is common ; therefore the whole , or the remainder AE , is equal to the whole , or the remainder DF ; ( ax . 2 or 3. ) and AB is equal to DC ; ( 1. 24 ...
Side 33
... reason , the parallelogram EFGH is equal to the parallelogram EBCH ; therefore the parallelogram ABCD is equal to the parallelogram EFGH . ( ax . 1. ) Therefore , parallelograms upon equal , & c . Q. E. D. PROPOSITION XXXVII . THEOREM ...
... reason , the parallelogram EFGH is equal to the parallelogram EBCH ; therefore the parallelogram ABCD is equal to the parallelogram EFGH . ( ax . 1. ) Therefore , parallelograms upon equal , & c . Q. E. D. PROPOSITION XXXVII . THEOREM ...
Side 37
... reason , the triangle KGC'is equal to the triangle KFC . Wherefore the two triangles AEK , KGC are equal to the two triangles AHK , KFC , ( ax . 2. ) but the whole triangle ABC is equal to the whole triangle ADC ; therefore the ...
... reason , the triangle KGC'is equal to the triangle KFC . Wherefore the two triangles AEK , KGC are equal to the two triangles AHK , KFC , ( ax . 2. ) but the whole triangle ABC is equal to the whole triangle ADC ; therefore the ...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ... Robert Potts Uten tilgangsbegrensning - 1845 |
Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson with ... Euclid,Robert Potts Uten tilgangsbegrensning - 1847 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 54 - If two triangles have two sides of the one equal to two sides of the...
Side 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...
Side 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.
Side 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.
Side 18 - Any two angles of a triangle are together less than two right angles.
Side 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.
Side 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.
Side 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.
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...