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 CambridgeLongman, Green, Longman, Roberts, & Green, 1865 - 504 sider |
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Side 67
... rectangle , and is said to be contained by any two of the straight lines which contain one of the right angles . II . In every parallelogram , any of the parallelograms about a diameter together with the two complements , is called a ...
... rectangle , and is said to be contained by any two of the straight lines which contain one of the right angles . II . In every parallelogram , any of the parallelograms about a diameter together with the two complements , is called a ...
Side 68
... rectangle BH is equal to the rectangles BK , DL , EH . And BH is contained by A and BC , for it is contained by GB , BC , of which GB is equal to A : and the rectangle BK is contained by A , BD , for it is contained by GB , BD , of ...
... rectangle BH is equal to the rectangles BK , DL , EH . And BH is contained by A and BC , for it is contained by GB , BC , of which GB is equal to A : and the rectangle BK is contained by A , BD , for it is contained by GB , BD , of ...
Side 69
... rectangle AE is equal to the rectangles AD , CE . And AE is the rectangle contained by AB , BC , for it is contained by AB , BĚ , of which BE is equal to BC : and AD is contained by AC , CB , for CD is équal to CB : and CE is the square ...
... rectangle AE is equal to the rectangles AD , CE . And AE is the rectangle contained by AB , BC , for it is contained by AB , BĚ , of which BE is equal to BC : and AD is contained by AC , CB , for CD is équal to CB : and CE is the square ...
Side 70
... rectangle contained by AC , CB , for GCis equal to CB ; therefore GE is also equal to the rectangle AC , CB ; wherefore AG , GE are equal to twice the rectangle AC , CB ; and HF , CK are the squares on AC , CB ; wherefore the four ...
... rectangle contained by AC , CB , for GCis equal to CB ; therefore GE is also equal to the rectangle AC , CB ; wherefore AG , GE are equal to twice the rectangle AC , CB ; and HF , CK are the squares on AC , CB ; wherefore the four ...
Side 71
... rectangle contained by AD , DB , for DH is equal to DB ; and DF together with CH is the gnomon CMG ; 14 therefore the gnomon CMG is equal to the rectangle AD , DB : to each of these equals add LG , which is equal to the square on CD ...
... rectangle contained by AD , DB , for DH is equal to DB ; and DF together with CH is the gnomon CMG ; 14 therefore the gnomon CMG is equal to the rectangle AD , DB : to each of these equals add LG , which is equal to the square on CD ...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ... Robert Potts Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side xiv - The sluggard is wiser in his own conceit than seven men that can render a reason.
Side 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...
Side 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.
Side 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 28 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.