The Elements of Euclid; viz. the first six books,together with the eleventh and twelfth, with an appendixThomas Tegg, 1841 - 351 σελίδες |
Αναζήτηση στο βιβλίο
Σελίδα 11
... two triangles have two sides of the one equal to two sides of the other ... triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle ...
... two triangles have two sides of the one equal to two sides of the other ... triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle ...
Σελίδα 15
Euclides William Rutherford. that the point B be on E , and the straight line ... side of it , there can be two triangles that have their sides which are ... triangle DEF ; then join AF : the straight line AF shall bisect the angle BAC . D F C ...
Euclides William Rutherford. that the point B be on E , and the straight line ... side of it , there can be two triangles that have their sides which are ... triangle DEF ; then join AF : the straight line AF shall bisect the angle BAC . D F C ...
Σελίδα 24
... ends of the side of a triangle , there be drawn two straight lines to a point within the tri- angle , these shall be less than the other two sides of the triangle , but shall contain a greater angle . Let ABC be a triangle , and from ...
... ends of the side of a triangle , there be drawn two straight lines to a point within the tri- angle , these shall be less than the other two sides of the triangle , but shall contain a greater angle . Let ABC be a triangle , and from ...
Σελίδα 26
... point A in the given straight line AB , that shall be equal to the given rectilineal angle DCE . A Да In CD , CE , take any points D D , E , and join DE ; and * 22. 1. make * the triangle ... lines CD , DE , CE , so that CD be equal to AF , ...
... point A in the given straight line AB , that shall be equal to the given rectilineal angle DCE . A Да In CD , CE , take any points D D , E , and join DE ; and * 22. 1. make * the triangle ... lines CD , DE , CE , so that CD be equal to AF , ...
Σελίδα 30
... straight line , falling upon two other straight lines , make the alternate angles equal to one another , these ... point G ; therefore GEF is a triangle , and its ex- 16. 1. terior angle AEF ... side of the line ; or make the interior angles ...
... straight line , falling upon two other straight lines , make the alternate angles equal to one another , these ... point G ; therefore GEF is a triangle , and its ex- 16. 1. terior angle AEF ... side of the line ; or make the interior angles ...
Άλλες εκδόσεις - Προβολή όλων
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AB is equal AC is equal altitude angle ABC angle ACB angle BAC base BC bisect centre circle ABCD circle EFGH circumference common section cone cylinder demonstrated described diameter draw equal to F equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prisms PROB proved pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD sphere square of AC straight line AC THEOR third three plane angles three straight lines tiples touches the circle triangle ABC triangle DEF triplicate ratio twice the rectangle wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 173 - 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 56 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Σελίδα 53 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Σελίδα 58 - IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Σελίδα 94 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 23 - Any two sides of a triangle are together greater than the third side.
Σελίδα 40 - EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels.
Σελίδα 103 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square on the line which touches it.
Σελίδα 50 - PROP. I. THEOR. If there oe two straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Σελίδα 28 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.