Question: What were Mendeleev's assertations concerning the first periodic table?
About the article "Atomic number", section "The periodic table and a natural number for each element".

Candidate passages:
Meyer is best known for the share he had in the periodic classification of the elements.
He noted, as did J.
A. R. Newlands in England, that if each one is arranged in the order of their atomic weights they fall into groups in that similar chemical and physical properties are repeated at periodic intervals; and in particular he showed that if the atomic weights are plotted as ordinates and the atomic volumes as abscissae, the curve obtained presents a series of maxima and minima, the most electro-positive elements appearing at the peaks of the curve in the order of their atomic weights.
His book on "Die modernen Theorien der Chemie", that was first published in Breslau in 1862 (The Internet Database of Periodic Tables.
Hemogenesis web book) and 1864, has an early version of the periodic table containing 28 elements classified into six families by their valence — the first time that elements had been grouped and ordered according to their valence.
Work on organizing the elements by atomic weight had hitherto been stymied by inaccurate measurements of the atomic weights.
Julius Lothar Meyer was the first to build the periodic table of elements.
Each obtained evidence of the priority of a German doctor, a chemist and physicist Julius Lothar von Meyer in the development of the Periodic Table.
He has published articles on his classification table of the elements in a horizontal form (1862, 1864) and vertical form (1870), where the series of periods are properly ended by an element of the earth metal group (Makeyev A.K.
Julius Lothar Meyer was first to build the periodic table of elements.
// Eropean applied sciences, April, 2013, 4 (2) - pp.
Mendeleev published his periodic table of all known elements (and predicted several new elements to complete the table, plus some corrected atomic weights) in 1869.
Working completely independently, a few months later, Meyer published a revised and expanded version of his 1864 table, virtually identical to that published by Mendeleev (Meyer had been sent a copy of Mendeleev's table earlier, Mendeleev sent it to all well known chemists of those times) and a paper showing graphically the periodicity of the elements as a function of atomic weight.
As well as other chemists, Meyer was doubtful about Mendeleev's periodic law, and he criticized Mendeleev for 'changing existing elements' atomic weights, only regarding possibility of periodical law in its structure', but Mendeleev's work provided significant support, particularly when the new elements were found as predicted and remeasured atomic weights accorded with those predicted.
In 1882, Meyer received from the Royal Society, at the same time as Mendeleev, the Davy Medal in recognition of his work on the Periodic Law. 
Unknown to Mendeleev, the German chemist Lothar Meyer was also working on a periodic table.
Although his work was published in 1864, and was done independently of Mendeleev, few historians regard him as an equal co-creator of the periodic table.
Meyer's table only included twenty-eight elements, which were not classified by atomic weight, but by valence and he never reached the idea of predicting new elements and correcting atomic weights.
A few months after Mendeleev published his periodic table of the known elements, predicted new elements to help complete his table and corrected the atomic weights of some of the elements, Meyer published a virtually identical periodic table.
Meyer and Mendeleev are considered by some historians of science to be the co-creators of the periodic table, but Mendeleev's accurate prediction of the qualities of undiscovered elements enables him to have the larger share of the credit. 
An important breakthrough in making sense of the list of known chemical elements (as well as in understanding the internal structure of atoms) was Dmitri Mendeleev's development of the first modern periodic table, or the periodic classification of the elements.
Mendeleev, a Russian chemist, felt that there was some type of order to the elements and he spent more than thirteen years of his life collecting data and assembling the concept, initially with the idea of resolving some of the disorder in the field for his students.
Mendeleev found that, when all the known chemical elements were arranged in order of increasing atomic weight, the resulting table displayed a recurring pattern, or periodicity, of properties within groups of elements.
Mendeleev's law allowed him to build up a systematic periodic table of all the 66 elements then known based on atomic mass, which he published in "Principles of Chemistry" in 1869.
His first Periodic Table was compiled on the basis of arranging the elements in ascending order of atomic weight and grouping them by similarity of properties.
Mendeleev had such faith in the validity of the periodic law that he proposed changes to the generally accepted values for the atomic weight of a few elements and, in his version of the periodic table of 1871, predicted the locations within the table of unknown elements together with their properties.
He even predicted the likely properties of three yet-to-be-discovered elements, which he called ekaboron (Eb), ekaaluminium (Ea), and ekasilicon (Es), which proved to be good predictors of the properties of scandium, gallium, and germanium, respectively, which each fill the spot in the periodic table assigned by Mendeleev.
At first the periodic system did not raise interest among chemists.
However, with the discovery of the predicted elements, notably gallium in 1875, scandium in 1879, and germanium in 1886, it began to win wide acceptance.
The subsequent proof of many of his predictions within his lifetime brought fame to Mendeleev as the founder of the periodic law.
This organization surpassed earlier attempts at classification by Alexandre-Émile Béguyer de Chancourtois, who published the telluric helix, an early, three-dimensional version of the periodic table of the elements in 1862, John Newlands, who proposed the law of octaves (a precursor to the periodic law) in 1864, and Lothar Meyer, who developed an early version of the periodic table with 28 elements organized by valence in 1864.
Mendeleev's table did not include any of the noble gases, however, which had not yet been discovered.
Gradually the periodic law and table became the framework for a great part of chemical theory.
By the time Mendeleyev died in 1907, he enjoyed international recognition and had received distinctions and awards from many countries.
In 1873, Jacobus Henricus van 't Hoff and Joseph Achille Le Bel, working independently, developed a model of chemical bonding that explained the chirality experiments of Pasteur and provided a physical cause for optical activity in chiral compounds.
van 't Hoff's publication, called V"oorstel tot Uitbreiding der Tegenwoordige in de Scheikunde gebruikte Structuurformules in de Ruimte", etc.
(Proposal for the development of 3-dimensional chemical structural formulae) and consisting of twelve pages text and one page diagrams, gave the impetus to the development of stereochemistry.
The concept of the "asymmetrical carbon atom", dealt with in this publication, supplied an explanation of the occurrence of numerous isomers, inexplicable by means of the then current structural formulae.
At the same time he pointed out the existence of relationship between optical activity and the presence of an asymmetrical carbon atom. 
Russian chemistry professor Dmitri Mendeleev and German chemist Julius Lothar Meyer independently published their periodic tables in 1869 and 1870, respectively.
Mendeleev's table was his first published version; that of Meyer was an expanded version of his (Meyer's) table of 1864.
They both constructed their tables by listing the elements in rows or columns in order of atomic weight and starting a new row or column when the characteristics of the elements began to repeat.
The recognition and acceptance afforded to Mendeleev's table came from two decisions he made.
The first was to leave gaps in the table when it seemed that the corresponding element had not yet been discovered.
Mendeleev was not the first chemist to do so, but he was the first to be recognized as using the trends in his periodic table to predict the properties of those missing elements, such as gallium and germanium.
The second decision was to occasionally ignore the order suggested by the atomic weights and switch adjacent elements, such as tellurium and iodine, to better classify them into chemical families.
With the development of theories of atomic structure, it became apparent that Mendeleev had unintentionally listed the elements in order of increasing atomic number or nuclear charge.
The significance of atomic numbers to the organization of the periodic table was not appreciated until the existence and properties of protons and neutrons became understood.
Mendeleev's periodic tables used atomic weight instead of atomic number to organize the elements, information determinable to fair precision in his time.
Atomic weight worked well enough in most cases to (as noted) give a presentation that was able to predict the properties of missing elements more accurately than any other method then known.
Substitution of atomic numbers, once understood, gave a definitive, integer-based sequence for the elements, still used today even as new synthetic elements are being produced and studied. 
The actinide concept in nuclear chemistry was first theorized by Glenn T. Seaborg in 1944, resulting in the extension of Dmitri Mendeleev's periodic table of the elements by placing a new actinide series, for elements 89–103, below the lanthanide series.
In later theoretical work, Seaborg proposed the transactinide series spanning elements 104–121 and the superactinide series containing elements 122–153.