The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illustrations, and an Appendix in Five BooksA. & C. Black, 1837 - 390 páginas |
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Página 4
... passes through the centre . 36. A segment of a circle is the figure contained by an arc and its chord . The chord is sometimes called the base of the segment . 37. A semicircle is a segment whose chord is a diameter . ‡ The following ...
... passes through the centre . 36. A segment of a circle is the figure contained by an arc and its chord . The chord is sometimes called the base of the segment . 37. A semicircle is a segment whose chord is a diameter . ‡ The following ...
Página 40
... pass , and which are called the complements of the other two , are equal . * E D A H F K B G C Let BD be a parallelogram , of which AC is one of the diagonals : then , if through K a point in AC , the two straight lines EF and HG be ...
... pass , and which are called the complements of the other two , are equal . * E D A H F K B G C Let BD be a parallelogram , of which AC is one of the diagonals : then , if through K a point in AC , the two straight lines EF and HG be ...
Página 64
... passes through the centre . Schol . The practical construction is very simply effected in the following manner : Take any three points A , B , C , in the circumference , and from A and B as cen- tres , with any radius greater than half ...
... passes through the centre . Schol . The practical construction is very simply effected in the following manner : Take any three points A , B , C , in the circumference , and from A and B as cen- tres , with any radius greater than half ...
Página 65
... pass through the centre , it cuts it at right angles ; and ( 2. ) if it cut it at right angles , it bisects it . Let ABC be a circle ; and let ED , a straight line drawn through the centre E , bisect any chord AB , which does not pass ...
... pass through the centre , it cuts it at right angles ; and ( 2. ) if it cut it at right angles , it bisects it . Let ABC be a circle ; and let ED , a straight line drawn through the centre E , bisect any chord AB , which does not pass ...
Página 66
... pass through the centre , it is plain that it can- not be bisected by the other which does not pass through the centre . But if neither of them pass through the centre , take ( III . 1. ) F the centre , and join EF ; and because FE , a ...
... pass through the centre , it is plain that it can- not be bisected by the other which does not pass through the centre . But if neither of them pass through the centre , take ( III . 1. ) F the centre , and join EF ; and because FE , a ...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol segments semicircle sides similar similar triangles solid angles square of AC straight lines drawn tangent THEOR third triangle ABC triplicate ratio vertex vertical angle wherefore
Pasajes populares
Página 94 - 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.
Página 53 - 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 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 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Página 57 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Página 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Página 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Página 32 - 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.
Página 40 - 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.
Página 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...