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 19
... consequently that all the angles made by any number of lines meeting in one point , are together equal to four right angles . PROP . XIV . THEOR . Ir , at a point in a straight line , two other straight lines on the opposite sides of it ...
... consequently that all the angles made by any number of lines meeting in one point , are together equal to four right angles . PROP . XIV . THEOR . Ir , at a point in a straight line , two other straight lines on the opposite sides of it ...
Página 26
... consequently the point H lies between D and F , and the line EG above EF . If , on the contrary , a line equal to DE the less side , were drawn through D , making with DF , on the same side of it with DE , an angle equal to A , the ...
... consequently the point H lies between D and F , and the line EG above EF . If , on the contrary , a line equal to DE the less side , were drawn through D , making with DF , on the same side of it with DE , an angle equal to A , the ...
Página 30
... consequently do not meet . Now , if through G a straight line be drawn in the angle BGH , and consequently making with GH an angle less than BGH , so that the two angles which GH makes with it and with HD are together less than two ...
... consequently do not meet . Now , if through G a straight line be drawn in the angle BGH , and consequently making with GH an angle less than BGH , so that the two angles which GH makes with it and with HD are together less than two ...
Página 37
... consequently less than two right angles . In like manner it might be shown that AD and CF will meet . The like reasoning is applicable in the next proposition . the triangle DEF of the parallelogram EH . But ( Book I. ] 37 OF EUCLID .
... consequently less than two right angles . In like manner it might be shown that AD and CF will meet . The like reasoning is applicable in the next proposition . the triangle DEF of the parallelogram EH . But ( Book I. ] 37 OF EUCLID .
Página 45
... consequently ( I. 46. cor . 3. ) AC and DF themselves are equal . Also , since the sides of the triangles are respectively equal , their angles ( I. 8. ) are likewise equal , each to each . The converse of this , that if the legs + of ...
... consequently ( I. 46. cor . 3. ) AC and DF themselves are equal . Also , since the sides of the triangles are respectively equal , their angles ( I. 8. ) are likewise equal , each to each . The converse of this , that if the legs + of ...
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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...