Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical GeometryW. E. Dean, 1845 - 317 σελίδες |
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Αποτελέσματα 1 - 5 από τα 19.
Σελίδα 106
... multiple of B by m . When the num- " ber is intended to multiply two or more magnitudes that follow , it is " written thus , m ( A + B ) , which signifies the sum of A and B taken m " times ; m ( A - B ) is m times the excess of A above ...
... multiple of B by m . When the num- " ber is intended to multiply two or more magnitudes that follow , it is " written thus , m ( A + B ) , which signifies the sum of A and B taken m " times ; m ( A - B ) is m times the excess of A above ...
Σελίδα 107
... multiple of the first is greater than the multiple of the second , equal to it , or less , the multiple of the third is also greater than the multiple of the fourth , equal to it , or less ; then the first of the magnitudes is said to ...
... multiple of the first is greater than the multiple of the second , equal to it , or less , the multiple of the third is also greater than the multiple of the fourth , equal to it , or less ; then the first of the magnitudes is said to ...
Σελίδα 109
... multiples , are equal to one another . 3. A multiple of a greater magnitude is greater than the same multiple of a less . 4. That magnitude of which a multiple is greater than the same multi- ple of another , is greater than that other ...
... multiples , are equal to one another . 3. A multiple of a greater magnitude is greater than the same multiple of a less . 4. That magnitude of which a multiple is greater than the same multi- ple of another , is greater than that other ...
Σελίδα 110
... multiple of D + E + F . COR . Hence , if m be any number , mD + mE + mF = m ( D + E + F ) . For mD , mE , and mF are multiples of D , E , and F by m , therefore their sum is also a multiple of D + E + F by m . PROP . II . THEOR . If to a ...
... multiple of D + E + F . COR . Hence , if m be any number , mD + mE + mF = m ( D + E + F ) . For mD , mE , and mF are multiples of D , E , and F by m , therefore their sum is also a multiple of D + E + F by m . PROP . II . THEOR . If to a ...
Σελίδα 111
... multiple of the second , that the multiple of the third has to the multiple of the fourth . Let A : B :: C : D , and let m and n be any two numbers ; mA : nB :: mC : nD . Take of mA and mC equimultiples by any number p , and of nB and ...
... multiple of the second , that the multiple of the third has to the multiple of the fourth . Let A : B :: C : D , and let m and n be any two numbers ; mA : nB :: mC : nD . Take of mA and mC equimultiples by any number p , and of nB and ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 50 - If a straight line be 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.
Σελίδα 51 - 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 of the line between the points of section, is equal to the square of half the line.
Σελίδα 16 - If two triangles have two sides of the one equal to two sides of the other...
Σελίδα 28 - 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 angle upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Σελίδα 13 - From the greater of two given straight lines to cut off a part equal to the less.
Σελίδα 9 - 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 52 - 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 on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Σελίδα 149 - ... cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 30 - 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 21 - Any two angles of a triangle are together less than two right angles, Let ABC be any triangle ; any two of its angles together are less than two right angles.