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 sider |
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Side 8
... circle ACE ; and from the point C , in which the circles cut one another , draw ( I. post . 1. ) the straight lines CA , CB to the points A , B : ABC is the equilateral triangle required . E Because the point A is the centre of the circle ...
... circle ACE ; and from the point C , in which the circles cut one another , draw ( I. post . 1. ) the straight lines CA , CB to the points A , B : ABC is the equilateral triangle required . E Because the point A is the centre of the circle ...
Side 64
... circles are those which contain equal angles . 9. Concentric circles are those which have the same centre . PROP . I. PROB . To find the centre of a given circle . Let ABC be the given circle ; it is required to find its centre . Draw ...
... circles are those which contain equal angles . 9. Concentric circles are those which have the same centre . PROP . I. PROB . To find the centre of a given circle . Let ABC be the given circle ; it is required to find its centre . Draw ...
Side 65
... circle . Let ABC be a circle , and A , B any two points in the circum- ference ; the chord drawn from A to B falls within the circle . A D E B Take any point in AB as E ; find ( III . 1. ) D the centre of the circle ABC ; join AD , DB ...
... circle . Let ABC be a circle , and A , B any two points in the circum- ference ; the chord drawn from A to B falls within the circle . A D E B Take any point in AB as E ; find ( III . 1. ) D the centre of the circle ABC ; join AD , DB ...
Side 66
... circles ABC , DEF in the points A , D , E , B ; AD is equal to EB , and AE to DB . From the com- mon centre G , draw GH perpendicular to AB . Then ( III . 3. ) AH is equal to HB , and DH to HE . From AH take DH , and from HB take HE ...
... circles ABC , DEF in the points A , D , E , B ; AD is equal to EB , and AE to DB . From the com- mon centre G , draw GH perpendicular to AB . Then ( III . 3. ) AH is equal to HB , and DH to HE . From AH take DH , and from HB take HE ...
Side 67
... circles ABC , DBE ; wherefore , if two circles , & c . PROP . VI . THEOR . If one circle touch another internally , they have not the same centre . Let the circle ABC be touched internally by the circle DEC in the point C : they have ...
... circles ABC , DBE ; wherefore , if two circles , & c . PROP . VI . THEOR . If one circle touch another internally , they have not the same centre . Let the circle ABC be touched internally by the circle DEC in the point C : they have ...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Side 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...