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 Seiten |
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Seite 24
... reason , the exterior angle CEB of the tri- angle ABE is greater than the angle BAE . But it has been shewn that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . Wherefore , if ...
... reason , the exterior angle CEB of the tri- angle ABE is greater than the angle BAE . But it has been shewn that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . Wherefore , if ...
Seite 39
... reason EF is equal to BC ; therefore AD is equal to EF ; B [ I. 34 . [ Axiom 1 . therefore the whole , or the remainder , AE is equal to the whole , or the remainder , DF . And AB is equal to DC ; [ Axioms 2 , 3 . [ I. 34 . therefore ...
... reason EF is equal to BC ; therefore AD is equal to EF ; B [ I. 34 . [ Axiom 1 . therefore the whole , or the remainder , AE is equal to the whole , or the remainder , DF . And AB is equal to DC ; [ Axioms 2 , 3 . [ I. 34 . therefore ...
Seite 40
... reason the parallelogram EFGH is equal to the same EBCH . Therefore the parallelogram ABCD is equal to the par- allelogram EFĜH . [ Axiom 1 . Wherefore , parallelograms & c . Q.E.D. PROPOSITION 37. THEOREM . Triangles on the same base ...
... reason the parallelogram EFGH is equal to the same EBCH . Therefore the parallelogram ABCD is equal to the par- allelogram EFĜH . [ Axiom 1 . Wherefore , parallelograms & c . Q.E.D. PROPOSITION 37. THEOREM . Triangles on the same base ...
Seite 45
... reason the triangle KGC is equal to the triangle KFC . Therefore , because the triangle AEK is equal to the tri- angle AHK , and the triangle KGC to the triangle KFC ; the triangle AEK together with the triangle KGC is equal to the ...
... reason the triangle KGC is equal to the triangle KFC . Therefore , because the triangle AEK is equal to the tri- angle AHK , and the triangle KGC to the triangle KFC ; the triangle AEK together with the triangle KGC is equal to the ...
Seite 50
... reason , AB and AH are in the same straight line . Now the angle DBC is equal to the angle FBA , for each of them is a right angle . Add to each the angle ABC . [ Axiom 11 . Therefore the whole angle DBA is equal to the whole angle FBC ...
... reason , AB and AH are in the same straight line . Now the angle DBC is equal to the angle FBA , for each of them is a right angle . Add to each the angle ABC . [ Axiom 11 . Therefore the whole angle DBA is equal to the whole angle FBC ...
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Häufige Begriffe und Wortgruppen
ABCD angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC BC is equal 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 radius 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
Beliebte Passagen
Seite 286 - 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.
Seite 30 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Seite 34 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Seite 37 - 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 together equal to two right angles.
Seite 12 - 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.
Seite 302 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Seite 220 - If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Seite 354 - 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.
Seite 104 - 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.
Seite 96 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.