Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J. Pryde. [With] Key1860 |
Inni boken
Resultat 6-10 av 50
Side 40
... taken , there remains the square BE , and if from the second there be taken the two equal triangles BAC and GAH , there remains the two squares GB and HC ; but BE is the square on BC , and GB and HC are the squares on AB and AC ...
... taken , there remains the square BE , and if from the second there be taken the two equal triangles BAC and GAH , there remains the two squares GB and HC ; but BE is the square on BC , and GB and HC are the squares on AB and AC ...
Side 41
... taken from any scale of equal parts , it is a right - angled triangle . For 52 32+ 42 , or 25 = 9 + 16 . PROPOSITION C. THEOREM . If two triangles have two sides and an angle opposite to one of them in the one , equal respectively to ...
... taken from any scale of equal parts , it is a right - angled triangle . For 52 32+ 42 , or 25 = 9 + 16 . PROPOSITION C. THEOREM . If two triangles have two sides and an angle opposite to one of them in the one , equal respectively to ...
Side 46
... taken in one of the angles , the sum of the perpendiculars from this point upon the sides that contain the angle , will be equal to a perpendicular from the point on the third line . 48. Given a point and three lines , two of which are ...
... taken in one of the angles , the sum of the perpendiculars from this point upon the sides that contain the angle , will be equal to a perpendicular from the point on the third line . 48. Given a point and three lines , two of which are ...
Side 65
... taken from half the sum , gives the less . For AD , DB ( 1st fig . ) are two unequal lines , AE is half their sum , and ED half their difference ; and AE + ED = AD , and AEED = DB . EXERCISES . 1. If from any point lines be drawn to the ...
... taken from half the sum , gives the less . For AD , DB ( 1st fig . ) are two unequal lines , AE is half their sum , and ED half their difference ; and AE + ED = AD , and AEED = DB . EXERCISES . 1. If from any point lines be drawn to the ...
Side 69
Euclides James Pryde. PROPOSITION II . THEOREM . If any two points be taken in the circumference of a circle , the straight line which joins them shall fall within the circle . Given a circle ABC , cumference ; to prove that B shall fall ...
Euclides James Pryde. PROPOSITION II . THEOREM . If any two points be taken in the circumference of a circle , the straight line which joins them shall fall within the circle . Given a circle ABC , cumference ; to prove that B shall fall ...
Andre utgaver - Vis alle
Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ... Euclides Uten tilgangsbegrensning - 1860 |
Euclid's Elements of Plane Geometry [Book 1-6] Explicitly Enunciated, by J ... Euclides,James Pryde Ingen forhåndsvisning tilgjengelig - 2023 |
Euclid's Elements of Plane Geometry [book 1-6] Explicitly Enunciated, by J ... Euclides,James Pryde Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
ABCD adjacent angles angle ABC angle ACB angle BAC apothem BA and AC base BC BC is equal bisected centre Chambers's chord circle ABC circumference Const cosec cosine described diameter divided double draw equal angles equal to twice equiangular equilateral polygon equimultiples exterior angle fore given line given point given straight line gnomon greater hence hypotenuse inscribed isosceles triangle less line drawn multiple number of sides opposite angle parallel parallelogram perimeter perpendicular polygon produced proportional PROPOSITION prove radius ratio rectangle contained rectilineal figure regular polygon remaining angle right angles right-angled triangle segment semiperimeter shewn similar sine square on AC straight line AC tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertical angle wherefore
Populære avsnitt
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. either the sides adjacent to the equal...
Side 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 of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Side 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 on the line between the points of section, is equal to the square on half the line.
Side 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 in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC...
Side 3 - 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 29 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 117 - And the same thing is to be understood when it is more briefly expressed by saying, a has to d the ratio compounded of the ratios of e to f, g to h, and k to l. In like manner, the same things being supposed, if m has to n the same ratio which a has to d ', then, for shortness...
Side 13 - 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.
Side 159 - From the point A draw a straight line AC, making any angle with AB ; and in AC take any point D, and take AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off. Because ED is parallel to one of the sides of the triangle ABC, viz. to BC ; as CD is to DA, so is (2.
Side 60 - CB, BA, by twice the rectangle CB, BD. Secondly, Let AD fall without the triangle ABC. Then, because the angle at D is a right angle, the angle ACB is greater than a right angle ; (i.