The Elements of Euclid, containing the first six books, with a selection of geometrical problems. To which is added the parts of the eleventh and twelfth books which are usually read at the universities. By J. Martin1874 |
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Seite 11
... angle BAC equal to the included angle EDF Then ( 1 ) shall the base BC be equal to the base EF ; and ( 2 ) the tri- angle ABC to the triangle DEF ; and ( 3 ) the other angles to which the equal sides are opposite shall be equal , each ...
... angle BAC equal to the included angle EDF Then ( 1 ) shall the base BC be equal to the base EF ; and ( 2 ) the tri- angle ABC to the triangle DEF ; and ( 3 ) the other angles to which the equal sides are opposite shall be equal , each ...
Seite 12
... angle BAC is equal to the angle EDF ; therefore also 3. The point C shall coincide with the point F , because AC is equal to DF . But the point B was shown to coincide with the point E ; wherefore , the base BC shall coincide with the ...
... angle BAC is equal to the angle EDF ; therefore also 3. The point C shall coincide with the point F , because AC is equal to DF . But the point B was shown to coincide with the point E ; wherefore , the base BC shall coincide with the ...
Seite 17
... angle ACD , the angles upon the other side of the base CD , namely , 1. The angles ECD , FDC are equal to one ... BAC shall be equal to the angle EDF . Demonstration . For , if the triangle ABC be applied to DEF , so that the point B be ...
... angle ACD , the angles upon the other side of the base CD , namely , 1. The angles ECD , FDC are equal to one ... BAC shall be equal to the angle EDF . Demonstration . For , if the triangle ABC be applied to DEF , so that the point B be ...
Seite 18
... Therefore if two triangles , & c . Q.E.D. PROPOSITION 9. - Problem . To bisect a given rectilineal angle , that is , to divide it into two equal angles . E Let BAC be the given rectilineal angle . It is 18 EUCLID'S ELEMENTS .
... Therefore if two triangles , & c . Q.E.D. PROPOSITION 9. - Problem . To bisect a given rectilineal angle , that is , to divide it into two equal angles . E Let BAC be the given rectilineal angle . It is 18 EUCLID'S ELEMENTS .
Seite 19
... angle BAC , Proof . Because AD is equal to AE ( constr . ) , and AF is common to the two triangles DAF , EAF , 1. The two sides DA , AF are equal to the two sides EA , AF , each to each ; and ( constr . ) therefore Wherefore 2. The base ...
... angle BAC , Proof . Because AD is equal to AE ( constr . ) , and AF is common to the two triangles DAF , EAF , 1. The two sides DA , AF are equal to the two sides EA , AF , each to each ; and ( constr . ) therefore Wherefore 2. The base ...
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The Elements of Euclid, Containing the First Six Books, with a Selection of ... Euclides Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
AC is equal adjacent angles angle ABC angle ACB angle BAC angle BCD angle DEF angle EDF angle equal base BC bisected centre circle ABC circumference constr Demonstration diameter double equal angles equal to F equiangular equilateral triangle equimultiples ex æquali exterior angle fourth given circle given point given straight line gnomon greater ratio inscribed less Let ABC Let the straight linear units meet multiple opposite angle parallel to BC parallelogram perpendicular plane polygon produced proportionals Q.E.D. PROPOSITION quadrilateral rectangle contained remaining angle right angles segment semicircle similar square on AC straight line AB straight line BC straight line drawn three straight lines tiple touches the circle triangle ABC triangle DEF twice the rectangle wherefore
Beliebte Passagen
Seite 1 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Seite 6 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Seite 232 - If two triangles, which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another, the remaining sides shall be in a straight line. Let...
Seite 112 - 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 209 - ... triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Seite 269 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Seite 199 - 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 23 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Seite 63 - 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...
Seite 32 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.