The Elements of geometry; or, The first six books, with the eleventh and twelfth, of Euclid, with corrections, annotations, and exercises, by R. Wallace. Cassell's ed1855 |
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Side 41
... gnomon . " Thus the parallelogram HG together with the comple- ments AF , F C , is a gnomon , which is more briefly ex- pressed by the letters A G K , or EH C , at the opposite angles of the parallelograms which make up the gnomon ...
... gnomon . " Thus the parallelogram HG together with the comple- ments AF , F C , is a gnomon , which is more briefly ex- pressed by the letters A G K , or EH C , at the opposite angles of the parallelograms which make up the gnomon ...
Side 44
... gnomon CMG . But AH is the rectangle AD.DB , for DH is equal to DB . Therefore the gnomon CMG is equal to the rectangle AD.DB. To each of these equals add LG , which is equal ( II . 4. Cor . ) to the square of CD . Therefore the gnomon ...
... gnomon CMG . But AH is the rectangle AD.DB , for DH is equal to DB . Therefore the gnomon CMG is equal to the rectangle AD.DB. To each of these equals add LG , which is equal ( II . 4. Cor . ) to the square of CD . Therefore the gnomon ...
Side 45
... gnomon CMG and LG make up the whole figure CF , which is the square of CB . Therefore the rectangle AD.DB , together ... gnomon CMG . But AM is the rectangle AD.DB , because DM is equal ( II . 4. Cor . ) to DB . Therefore the gnomon CMG ...
... gnomon CMG and LG make up the whole figure CF , which is the square of CB . Therefore the rectangle AD.DB , together ... gnomon CMG . But AM is the rectangle AD.DB , because DM is equal ( II . 4. Cor . ) to DB . Therefore the gnomon CMG ...
Side 46
... gnomon AKF and the square CK . Therefore the gnomon AK F and the square CK are together double of A K. But twice the rect- angle A B.BC , is double of AK , for BK is equal ( II . 4 Cor . ) to B C. Therefore the gnomon AK F and the ...
... gnomon AKF and the square CK . Therefore the gnomon AK F and the square CK are together double of A K. But twice the rect- angle A B.BC , is double of AK , for BK is equal ( II . 4 Cor . ) to B C. Therefore the gnomon AK F and the ...
Side 47
... gnomon AOH is four times the rectangle AK ; that is , four times the rectangle AB . BC , because BK is equal to B C. To these equals , add the square of A C , or its equal the square XH ( I. 34 ) . Therefore four times the rectangle AB ...
... gnomon AOH is four times the rectangle AK ; that is , four times the rectangle AB . BC , because BK is equal to B C. To these equals , add the square of A C , or its equal the square XH ( I. 34 ) . Therefore four times the rectangle AB ...
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The Elements of Geometry: Or, the First Six Books, with the Eleventh and ... Euclides Ingen forhåndsvisning - 2016 |
Almindelige termer og sætninger
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle DEF angle EDF base BC bisected centre circle ABC circumference cone cylinder described diagonal diameter draw duplicate ratio equal angles equal Ax equal Const equiangular equimultiples Euclid ex æquali Exercise exterior angle fore given straight line gnomon homologous sides inscribed join less meet multiple opposite angle parallelogram parallelogram AC parallelopiped pentagon perpendicular polygon prism produced proposition Q. E. D. PROP reciprocally proportional rectangle contained rectilineal figure remaining angle right angles segment similar triangles solid angle sphere squares of AC straight line drawn straight lines A B THEOREM third three plane angles three straight lines triangle ABC triangle DEF triplicate ratio twice the rectangle vertex Wherefore whole angle
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Side 23 - 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 34 - If there be 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.
Side 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Side 122 - 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 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 3 - 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.
Side 135 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.
Side 20 - PROBLEM. At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle.
Side 147 - Similar solid figures are such as have all their solid angles equal, each to each, and are contained by the same number of similar planes.
Side 37 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...