The Elements of Euclid: viz. the first six books, together with the eleventh and twelfth; and also the book of Euclid's DataBell & Bradfute, 1835 - 513 σελίδες |
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Σελίδα 13
... divided into two equal parts in the point D. Which was to be done . C A PROP . XI . PROB . C Book I. c 4. 1 . D B To draw a straight line at right angles to a given straight line , from a given point in the same . Let AB be a given ...
... divided into two equal parts in the point D. Which was to be done . C A PROP . XI . PROB . C Book I. c 4. 1 . D B To draw a straight line at right angles to a given straight line , from a given point in the same . Let AB be a given ...
Σελίδα 28
... divided into as many triangles as the figure has sides , by drawing straight lines from a point F within the figure to each of its angles . And , by D F A B Book I. the preceding proposition , all the angles of THE ELEMENTS.
... divided into as many triangles as the figure has sides , by drawing straight lines from a point F within the figure to each of its angles . And , by D F A B Book I. the preceding proposition , all the angles of THE ELEMENTS.
Σελίδα 42
... di- vided into any number of parts ; the rectangle con- tained by the two straight lines is equal to the rect- angles contained by the undivided line , and the seve- ral parts of the divided line . B DEC Let A and BC be two straight lines.
... di- vided into any number of parts ; the rectangle con- tained by the two straight lines is equal to the rect- angles contained by the undivided line , and the seve- ral parts of the divided line . B DEC Let A and BC be two straight lines.
Σελίδα 43
... divided into any two parts , the rectangles contained by the whole and each of the parts , are together equal to the square of the whole line . Let the straight line AB be divided into any two parts in the point C ; the A rectangle ...
... divided into any two parts , the rectangles contained by the whole and each of the parts , are together equal to the square of the whole line . Let the straight line AB be divided into any two parts in the point C ; the A rectangle ...
Σελίδα 44
... divided into any two parts , the square of the whole line is equal to the squares of the two parts , together with twice the rectangle contained by the parts . Let the straight line AB be divided into any two parts in C ; the square of ...
... divided into any two parts , the square of the whole line is equal to the squares of the two parts , together with twice the rectangle contained by the parts . Let the straight line AB be divided into any two parts in C ; the square of ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle BAC arch base BC BC is equal BC is given bisected Book XI centre circle ABC circumference cone cosine cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles gnomon greater half the perimeter hypotenuse join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelepiped spherical angle square of AC straight line AB straight line BC tangent THEOR tiple triangle ABC vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 95 - 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 153 - 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 306 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Σελίδα 11 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
Σελίδα 11 - 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 equal to one another, and likewise those which are terminated in the other extremity.
Σελίδα 317 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 54 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Σελίδα 26 - IF a straight line fall upon two parallel straight lines it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite, upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Σελίδα 11 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 93 - A circle is said to be described about a rectilineal figure, when the circumference of the circle passes through all the angular points of the figure about which it is described. VII. A straight line is said to be placed in a circle, when the extremities of it are in the circumference of the circle.