Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Appendix by Thos. Kirkland. the first six booksA. Miller & Company, 1876 - 403 Seiten |
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Seite 9
... remaining angles of one triangle coincide with the remain- ing angles of the other , and are equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . Therefore , if two triangles have two sides of the one equal ...
... remaining angles of one triangle coincide with the remain- ing angles of the other , and are equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . Therefore , if two triangles have two sides of the one equal ...
Seite 10
... remaining angles of the one are equal to the remaining angles of the other , each to each , to which the equal sides are opposite ; viz . the angle ACF to the angle ABG , and the angle AFC to the angle AGB . And because the whole AF is ...
... remaining angles of the one are equal to the remaining angles of the other , each to each , to which the equal sides are opposite ; viz . the angle ACF to the angle ABG , and the angle AFC to the angle AGB . And because the whole AF is ...
Seite 16
... remaining angle ABE is equal to the remaining angle ABD ; ( ax . 3. ) the less angle equal to the greater , which is impossible : therefore BE is not in the same straight line with BC . And in the same manner it may be demonstrated ...
... remaining angle ABE is equal to the remaining angle ABD ; ( ax . 3. ) the less angle equal to the greater , which is impossible : therefore BE is not in the same straight line with BC . And in the same manner it may be demonstrated ...
Seite 17
... remaining angle CEA is equal to the remaining angle DEB . · ( ax . 3. ) In the same manner it may be demonstrated , that the angle CEB is equal to the angle AED . Therefore , if two straight lines cut one another , & c . Q. E.D. COR . 1 ...
... remaining angle CEA is equal to the remaining angle DEB . · ( ax . 3. ) In the same manner it may be demonstrated , that the angle CEB is equal to the angle AED . Therefore , if two straight lines cut one another , & c . Q. E.D. COR . 1 ...
Seite 18
... remaining angles of one triangle to the remaining angles of the other , each to each , to which the equal sides are opposite ; wherefore the angle BAE is equal to the angle ECF ; but the angle ECD or ACD is greater than the angle ECF ...
... remaining angles of one triangle to the remaining angles of the other , each to each , to which the equal sides are opposite ; wherefore the angle BAE is equal to the angle ECF ; but the angle ECD or ACD is greater than the angle ECF ...
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Häufige Begriffe und Wortgruppen
A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC angle equal Apply Euc base BC chord circle ABC constr describe a circle diagonals diameter divided draw equal angles equiangular equilateral triangle equimultiples Euclid exterior angle Geometrical given circle given line given point given straight line gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line BC lines be drawn multiple opposite angles parallelogram parallelopiped pentagon perpendicular plane polygon produced Prop proportionals proved Q.E.D. PROPOSITION quadrilateral quadrilateral figure radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar similar triangles solid angle square on AC tangent THEOREM touch the circle triangle ABC twice the rectangle vertex vertical angle wherefore
Beliebte Passagen
Seite 93 - If a straight line be bisected and produced to any point, the square on the whole line thus produced, and the square on the part of it produced, are together double of the square on half the line bisected, and of the square on the line made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to D ; The squares on AD and DB shall be together double of the squares on AC and CD. CONSTRUCTION. — From the point C draw CE at right angles to AB, and make it equal...
Seite 118 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
Seite 145 - 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.
Seite 88 - 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.
Seite 26 - ... upon the same side together equal to two right angles, the two straight lines shall be parallel to one another.
Seite 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Seite 144 - 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 92 - 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 xv - In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Seite 67 - A proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate or capable of innumerable solutions.