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, 1883 - 400 sider |
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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 . Then the angle ACB is greater But this is impossible , because than the angle ABC , by T. 18 . 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 . Then the angle ACB is greater But this is impossible , because than the angle ABC , by T. 18 . 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 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
Populære avsnitt
Side 262 - 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.
Side 71 - 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 262 - To draw a straight line at right angles to a given straight line, from a given point in the same. Let AB be...
Side 182 - 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 8 - 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 298 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Side 58 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 60 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts in the point D ; The squares on AD and DB shall be together double of AD»+DB
Side 242 - Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so at length to become greater than AB.
Side 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.