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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Resultat 1-5 av 43
Side 162
... Suppose that HO and MP are equal to BE and DF . Then , because AE is to EB as CF is to FD , [ Hypothesis . and that GK and LN are equimultiples of AE and CF ; therefore GK is to EB as LN is to FD . [ V. 4 , Cor . But HO is equal to BE ...
... Suppose that HO and MP are equal to BE and DF . Then , because AE is to EB as CF is to FD , [ Hypothesis . and that GK and LN are equimultiples of AE and CF ; therefore GK is to EB as LN is to FD . [ V. 4 , Cor . But HO is equal to BE ...
Side 163
... suppose that HO and MP are equimultiples of EB and FD . Then , because AE is to EB as CF is to FD ; [ Hypothesis . and that GK and LN are equimultiples of AE and CF , and HO and MP are equi- multiples of EB and FD ; therefore if GK be ...
... suppose that HO and MP are equimultiples of EB and FD . Then , because AE is to EB as CF is to FD ; [ Hypothesis . and that GK and LN are equimultiples of AE and CF , and HO and MP are equi- multiples of EB and FD ; therefore if GK be ...
Side 255
... one of them must be greater than the other ; suppose AB greater than AC . than the angle ABC , by I. 18 . Then the angle ACB is greater But this is impossible , becauso the angle ACB is equal to the angle ABC , EUCLID'S ELEMENTS . 255.
... one of them must be greater than the other ; suppose AB greater than AC . than the angle ABC , by I. 18 . Then the angle ACB is greater But this is impossible , becauso the angle ACB is equal to the angle ABC , EUCLID'S ELEMENTS . 255.
Side 258
... suppose , if possible , that it takes a different position as AK . Then the angle DAK is equal to the angle HEF , and the angle CAK to the angle GEF ; but the angles HEF and GEF are equal , by hypothesis ; therefore the angles DAK and ...
... suppose , if possible , that it takes a different position as AK . Then the angle DAK is equal to the angle HEF , and the angle CAK to the angle GEF ; but the angles HEF and GEF are equal , by hypothesis ; therefore the angles DAK and ...
Side 261
... suppose the straight line FB drawn ; then in the two triangles FBE , FBD , the side FB and the angle FBC are common , and the side FE is equal to the side FD , but the triangles are not equal in all respects . In certain cases , however ...
... suppose the straight line FB drawn ; then in the two triangles FBE , FBD , the side FB and the angle FBC are common , and the side FE is equal to the side FD , but the triangles are not equal in all respects . In certain cases , however ...
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.