Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson...together with a Selection of Geometrical Exercises from the Senate-house and College Examination Papers .... the first six books, and the portions of the eleventh and twelfth books read at Cambridge
Longman, Green, Longman, Roberts, & Green, 1865 - 504 Seiten
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A₁ ABCD AC is equal angle ABC angle ACB angle BAC angle equal Apply Euc base BC bisects the angle chord circle ABC circle described circle whose center circles touch circumscribing circle construction describe a circle diagonals diameter divided draw equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements exterior angle Geometrical given circle given line given point given straight line greater hypotenuse isosceles triangle Let ABC line joining lines be drawn meet the circumference multiple opposite angles parallelogram parallelopiped pentagon perpendicular plane point of contact polygon produced Prop proved Q.E.D. PROPOSITION quadrilateral quadrilateral figure radius rectangle contained rectilineal figure right angles right-angled triangle segment semicircle shew shewn similar triangles solid angle square on AC tangent THEOREM touch the circle triangle ABC vertex vertical angle wherefore
Seite 23 - 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.
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 29 - All the interior angles of any rectilineal figure together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 71 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Seite 15 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it, the angles CBA, ABD : these shall either be two right angles, or shall together be equal to two right angles. For...
Seite 242 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Seite 2 - 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 34 - Equal triangles, upon equal bases in the same straight line, and towards the same parts, are between the same parallels. Let the equal triangles ABC, DEF be upon equal bases BC, EF, in the same straight line BF, and towards the same parts.