The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 Seiten |
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Seite 86
... difference between any two sides of a triangle is less than the third side . 6. Given two points C , D and a straight line AB , find P in AB such that the difference between PC and PD is as long as possible . 7. Any two sides of a ...
... difference between any two sides of a triangle is less than the third side . 6. Given two points C , D and a straight line AB , find P in AB such that the difference between PC and PD is as long as possible . 7. Any two sides of a ...
Seite 112
... difference between the angles at B , C. 12. An angle of a triangle is acute , right or obtuse according as it is less than , equal to or greater than the other two angles together . 13. D is the middle point of the side BC of a triangle ...
... difference between the angles at B , C. 12. An angle of a triangle is acute , right or obtuse according as it is less than , equal to or greater than the other two angles together . 13. D is the middle point of the side BC of a triangle ...
Seite 137
... difference of the areas PAB , PAD . P B A M B DN M A N Join AP . Let BM , CN parallels to PA , cut AD in M and N respectively . Then the triangles ABM , DCN are equiangular ; also , by Prop . 34 , AB DC ; therefore , by Prop . 26 , AM ...
... difference of the areas PAB , PAD . P B A M B DN M A N Join AP . Let BM , CN parallels to PA , cut AD in M and N respectively . Then the triangles ABM , DCN are equiangular ; also , by Prop . 34 , AB DC ; therefore , by Prop . 26 , AM ...
Seite 145
... difference of the areas of PAB , PCD is half the area of the parallelogram ABCD . 4. If P be a point within a parallelogram ABCD the sum of the areas of PAB , PCD is equal to the sum of the areas of PAD , PBC . 5. ABCD is a ...
... difference of the areas of PAB , PCD is half the area of the parallelogram ABCD . 4. If P be a point within a parallelogram ABCD the sum of the areas of PAB , PCD is equal to the sum of the areas of PAD , PBC . 5. ABCD is a ...
Seite 147
... difference of the areas ABML , AEFD is twice the area APC . 6. ABCD is a parallelogram and P is any point within it ; prove that the difference of the areas of APB , APD is that of APC . 7. P , Q are points in the diagonal of a ...
... difference of the areas ABML , AEFD is twice the area APC . 6. ABCD is a parallelogram and P is any point within it ; prove that the difference of the areas of APB , APD is that of APC . 7. P , Q are points in the diagonal of a ...
Häufige Begriffe und Wortgruppen
ABC is equal adjacent angles alternate angles angle ABC angle ACB angle BAC angle equal angles FAB angular point area of ABC base BC bisectors bisects the angle centre coincide Consider the triangles Construction corresponding angle DEF are equal describe a triangle diagonal equal angles equal area equal in area equal respectively equal to BC equidistant equilateral triangle exterior angle finite straight line given angle given finite straight given parallelogram given point given straight line given triangle greater included angle interior opposite angle intersect isosceles triangle line BC middle point opposite sides perpendicular plane produced Prop Proposition Q.E.D. EXAMPLES quadrilateral radius rectilineal figure required to prove rhombus right angles right-angled triangle Shew side BC sides equal square straight angle surface third side triangle ABC triangle DEF triangles are equal Wherefore
Beliebte Passagen
Seite 28 - 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.
Seite 72 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Seite 48 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Seite 151 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Seite 118 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Seite 149 - ... is equal to the sum of the areas of the squares on the other two sides.
Seite 114 - 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.
Seite 135 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Seite 125 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Seite 54 - To draw a straight line at right angles to a given straight line, from a given point in the same.