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 σελίδες |
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Σελίδα 12
... Hence every equilateral triangle is also equiangular . This is shown by taking , first , one side as base , and then another . * In this proposition , the hypothesis is , that the triangle under consideration has two of its sides equal ...
... Hence every equilateral triangle is also equiangular . This is shown by taking , first , one side as base , and then another . * In this proposition , the hypothesis is , that the triangle under consideration has two of its sides equal ...
Σελίδα 14
... Hence every equiangular triangle is also equilateral . PROP . VII . THEOR . * C UPON the same base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of the base ...
... Hence every equiangular triangle is also equilateral . PROP . VII . THEOR . * C UPON the same base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of the base ...
Σελίδα 31
... Hence , if there be two parallels , a straight line which intersects one of them , will intersect the other , if continually pro- duced . Thus , if any straight line be drawn through G , intersect- ing AB , the angles which it and CD ...
... Hence , if there be two parallels , a straight line which intersects one of them , will intersect the other , if continually pro- duced . Thus , if any straight line be drawn through G , intersect- ing AB , the angles which it and CD ...
Σελίδα 33
... Hence , a right angle may be trisected by describing an equilateral triangle on one of the lines containing the right angle . + while each of the other triangles has only one side of the figure for one of its sides ; and hence the ...
... Hence , a right angle may be trisected by describing an equilateral triangle on one of the lines containing the right angle . + while each of the other triangles has only one side of the figure for one of its sides ; and hence the ...
Σελίδα 38
... Hence a straight line drawn from the vertex of a triangle to the point of bisection of the base , bisects the triangle : and if two triangles have two sides of the one respectively equal to two sides of the other , and the contained ...
... Hence a straight line drawn from the vertex of a triangle to the point of bisection of the base , bisects the triangle : and if two triangles have two sides of the one respectively equal to two sides of the other , and the contained ...
Άλλες εκδόσεις - Προβολή όλων
The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...