Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books and the First Twenty-one Propositions of the Eleventh Book ...T. Stevenson, 1845 - 199 páginas |
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Página 6
... whole is greater than its part . X. Two straight lines cannot inclose a space . XI . All right angles are equal to one another . XII . " If a straight line meets two straight lines , so as to make " the two interior angles on the same ...
... whole is greater than its part . X. Two straight lines cannot inclose a space . XI . All right angles are equal to one another . XII . " If a straight line meets two straight lines , so as to make " the two interior angles on the same ...
Página 9
... whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it§ ; and the § 8 Ax . other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the ...
... whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it§ ; and the § 8 Ax . other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the ...
Página 10
... whole AF is equal to the whole AG § , of which the parts AB , AC , are equal¶ ; the remainder BF shall be equal * to the remainder CG ; and FC was proved to be equal to GB ; therefore the two sides BF , FC are equal to the two CG , GB ...
... whole AF is equal to the whole AG § , of which the parts AB , AC , are equal¶ ; the remainder BF shall be equal * to the remainder CG ; and FC was proved to be equal to GB ; therefore the two sides BF , FC are equal to the two CG , GB ...
Página 28
... whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; To these equals add the angle ACB , and the angles ACD , ACB are equal to the three angles CBA , BAC , ACB ; but the angles ACD , ACB are equal to two ...
... whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; To these equals add the angle ACB , and the angles ACD , ACB are equal to the three angles CBA , BAC , ACB ; but the angles ACD , ACB are equal to two ...
Página 30
... whole angle ABD is equal to the whole angle ACD : and the angle BAC has been shown to be equal to the angle BDC ; therefore the opposite sides and angles of parallelograms are equal to one another ; Also , their diameter bisects them ...
... whole angle ABD is equal to the whole angle ACD : and the angle BAC has been shown to be equal to the angle BDC ; therefore the opposite sides and angles of parallelograms are equal to one another ; Also , their diameter bisects them ...
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Términos y frases comunes
ABCD adjacent angles angle ABC angle ACB angle BAC angle BCD angle DEF angle EDF angles equal base BC BC is equal bisected centre circle ABC Constr describe diameter double draw equal angles equal to F equiangular equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio join less Let ABC Let the straight likewise meet multiple opposite angle parallel to BC parallelogram perpendicular plane polygon proportionals Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle sides square of AC straight line AB straight line AC THEOR THEOR.-If three straight lines tiple touches the circle triangle ABC triangle DEF twice the rectangle wherefore
Pasajes populares
Página 12 - If two triangles have two sides of the one equal to two sides of the...
Página 29 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Página 143 - 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.
Página 69 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Página 20 - If from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let the two straight lines BD.
Página 102 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater; that is, ' when the less is contained a certain number of times
Página 44 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Página 71 - The opposite angles of any quadrilateral figure described in a circle, are toe/ether equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD : any two of its opposite angles are together equal to two right angles.
Página 66 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Página 83 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.