The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books : with Notes, an Appendix, and ExercisesMacmillan, 1867 - 400 sider |
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Side 11
... shewn to be equal to GB ; therefore the two sides BF , FC are equal to the two sides CG , GB , each to each ; and the angle BFC was shewn to be equal to the angle CGB ; therefore the triangles BFC , CGB are equal , and their other ...
... shewn to be equal to GB ; therefore the two sides BF , FC are equal to the two sides CG , GB , each to each ; and the angle BFC was shewn to be equal to the angle CGB ; therefore the triangles BFC , CGB are equal , and their other ...
Side 13
... shewn to be greater ; which is impossible . But if one of the vertices as D , be within the other triangle ACB , produce AC , AD to E , F. Then because AC is equal to AD , in the triangle ACD , [ Hyp . the angles ECD , FDC , on the ...
... shewn to be greater ; which is impossible . But if one of the vertices as D , be within the other triangle ACB , produce AC , AD to E , F. Then because AC is equal to AD , in the triangle ACD , [ Hyp . the angles ECD , FDC , on the ...
Side 20
... shewn to be toge- ther equal to two right angles . Therefore the angles CEA , AED are equal to the angles AED , DEB . From each of these equals take away the common_angle AED , and the remaining angle CEA is equal to the re- maining ...
... shewn to be toge- ther equal to two right angles . Therefore the angles CEA , AED are equal to the angles AED , DEB . From each of these equals take away the common_angle AED , and the remaining angle CEA is equal to the re- maining ...
Side 21
... shewn that the angle BCG , that is the angle ACD , is greater than the angle ABC . [ I. 15 . Wherefore , if one side & c . Q.E.D. PROPOSITION 17. THEOREM . Any two angles of a triangle are together less than two right angles . Let ABC ...
... shewn that the angle BCG , that is the angle ACD , is greater than the angle ABC . [ I. 15 . Wherefore , if one side & c . Q.E.D. PROPOSITION 17. THEOREM . Any two angles of a triangle are together less than two right angles . Let ABC ...
Side 23
... shewn that AC is not equal to AB . Therefore AC is greater than AB . Wherefore , the greater angle & c . Q.E.D. PROPOSITION 20 . THEOREM . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle ...
... shewn that AC is not equal to AB . Therefore AC is greater than AB . Wherefore , the greater angle & c . Q.E.D. PROPOSITION 20 . THEOREM . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle ...
Andre utgaver - Vis alle
The Elements of Euclid for the Use of Schools and Colleges Isaac Todhunter Uten tilgangsbegrensning - 1872 |
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... Euclid,Isaac Todhunter Uten tilgangsbegrensning - 1884 |
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... Euclid,Isaac Todhunter Uten tilgangsbegrensning - 1867 |
Vanlige uttrykk og setninger
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore
Populære avsnitt
Side 35 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Side 67 - 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 upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle, Let ABC be an obtuse-angled triangle, having the obtuse angle...
Side 73 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.
Side 284 - 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 50 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Side 57 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Side 10 - 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.
Side 227 - If two straight lines be at right angles to the same plane, they shall be parallel to one another. Let the straight lines AB, CD be at right angles to the same plane : AB is parallel to CD.
Side 102 - 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 352 - Prove that the square on any straight line drawn from the vertex of an isosceles triangle to the base, is less than the square on a side of the triangle by the rectangle contained by the segments of the base : and conversely.