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 σελίδες |
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Αποτελέσματα 1 - 5 από τα 37.
Σελίδα 10
... fall on DF , because the angle BAĆ is equal to the angle EDF . B [ Hypothesis . Therefore also the point C will coincide with the point F , because AC is equal to DF . [ Hypothesis . But the point B was shewn to coincide with the point ...
... fall on DF , because the angle BAĆ is equal to the angle EDF . B [ Hypothesis . Therefore also the point C will coincide with the point F , because AC is equal to DF . [ Hypothesis . But the point B was shewn to coincide with the point ...
Σελίδα 30
... [ Hypothesis . therefore the base AC is equal to the base DF , and the third angle BAC to the third angle EDF . Wherefore , if two triangles & c . Q.E.D. [ I. 4 . PROPOSITION 27. THEOREM . · If a straight line falling 30 EUCLID'S ELEMENTS .
... [ Hypothesis . therefore the base AC is equal to the base DF , and the third angle BAC to the third angle EDF . Wherefore , if two triangles & c . Q.E.D. [ I. 4 . PROPOSITION 27. THEOREM . · If a straight line falling 30 EUCLID'S ELEMENTS .
Σελίδα 31
... falling on two other straight lines , make the alternate angles equal to one another , the two straight lines shall be parallel to one another . Let the straight line EF , which falls on the two straight lines AB , CD , make the ...
... falling on two other straight lines , make the alternate angles equal to one another , the two straight lines shall be parallel to one another . Let the straight line EF , which falls on the two straight lines AB , CD , make the ...
Σελίδα 32
... fall on two parallel straight lines , it makes the alternate angles equal to one another , and the exterior angle equal to the interior and opposite angle on the same side ; and also the two interior angles on the same side together ...
... fall on two parallel straight lines , it makes the alternate angles equal to one another , and the exterior angle equal to the interior and opposite angle on the same side ; and also the two interior angles on the same side together ...
Σελίδα 35
... falls on them , the alternate angles B BAC , ACE are equal . [ I. 29 . Again , because AB is parallel to CE , and BD falls on them , the exterior angle ECD is equal to the interior and opposite angle ABC . [ I. 29 . But the angle ACE ...
... falls on them , the alternate angles B BAC , ACE are equal . [ I. 29 . Again , because AB is parallel to CE , and BD falls on them , the exterior angle ECD is equal to the interior and opposite angle ABC . [ I. 29 . But the angle ACE ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 262 - To draw a straight line at right angles to a given straight line, from a given point in the same. Let AB be...
Σελίδα 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.
Σελίδα 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.
Σελίδα 298 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Σελίδα 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.
Σελίδα 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
Σελίδα 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.
Σελίδα 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.